Verfügbarkeit: Introduction to robust estimation and hypothesis testing

Introduction to robust estimation and hypothesis testing:

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Bibliographische Detailangaben
1. Verfasser:	Wilcox, Rand R. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Amsterdam [u.a.] Elsevier Acad. Press 2005
Ausgabe:	2. ed.
Schlagworte:	Robuustheid Schattingstheorie Statistische toetsen Estimation theory Robust statistics Statistical hypothesis testing Robuste Schätzung Statistischer Test
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XIX, 588 S. graph. Darst.
ISBN:	0127515429

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245	1	0	\|a Introduction to robust estimation and hypothesis testing \|c Rand R. Wilcox
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Datensatz im Suchindex

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adam_text	Contents Preface ................................................................. xvii Chapter I Introduction .............................................. I 1.1 Problems with Assuming Normality ................................ 2 1.2 Transformations .................................................... 6 1.3 The Influence Curve ................................................ 7 1.4 The Central Limit Theorem ......................................... 8 1.5 Is the ANOVA F Robust? ........................................... 9 1.6 Regression .......................................................... 10 1.7 More Remarks ...................................................... 10 1.8 Using the Computer: R and S-PLUS ................................. 11 1.9 Some Data-Managment Issues ...................................... 13 1.9.1 Eliminating Missing Values ................................ 17 Chapter 2 A Foundation for Robust Methods ........................ 19 2.1 Basic Tools for Judging Robustness ................................. 20 2.1.1 Qualitative Robustness .................................... 21 2.1.2 Infinitesimal Robustness ................................... 23 2.1.3 Quantitative Robustness ................................... 25 2.2 Some Measures of Location and Their Influence Function ........... 26 2.2.1 Quantiles .................................................. 26 2.2.2 The Winsorized Mean ..................................... 27 iii /v Contents 2.2.3 The Trimmed Mean ....................................... 29 2.2.4 M-Measures of Location ................................... 30 2.2.5 R-Measures of Location .................................... 33 2.3 Measures of Scale ................................................... 33 2.3.1 Mean Deviation from the Mean ............................ 34 2.3.2 Mean Deviation from the Median .......................... 35 2.3.3 Median Absolute Deviation ................................ 35 2.3.4 The (j-Quantile Range ...................................... 35 2.3.5 The Winsorized Variance .................................. 36 2.4 Scale-Equivariant M-Measures of Location .......................... 36 2.5 Winsorized Expected Values ........................................ 38 Chapter 3 Estimating Measures of Location and Scale .............. 43 3.1 A Bootstrap Estimate of a Standard Error ........................... 44 3.1.1 R and S-PLUS Function bootse ............................ 46 3.2 Density Estimators ................................................. 47 3.2.1 Normal Kernel ............................................ 47 3.2.2 Rosenblatt s Shifted Histogram ............................ 48 3.2.3 The Expected Frequency Curve ............................ 48 3.2.4 An Adaptive Kernel Estimator ............................. 49 3.2.5 R and S-PLUS Functions skerd, kerden, kdplot, rdplot, akerd, and splot .......................................... 50 3.3 The Sample Trimmed Mean ......................................... 56 3.3.1 R and S-PLUS Function tmean ............................. 59 3.3.2 Estimating the Standard Error of the Trimmed Mean ....... 59 3.3.3 R and S-PLUS Functions win, winvar, and trimse .......... 64 3.3.4 Estimating the Standard Error of the Sample Median, M ... 64 3.3.5 R and S-PLUS Function msmedse ........................... 65 3.4 The Finite-Sample Breakdown Point ................................ 65 3.5 Estimating Quantiles ............................................... 66 3.5.1 Estimating the Standard Error of the Sample Quantile ...... 67 3.5.2 R and S-PLUS Function qse ................................ 69 3.5.3 The Maritz-Jarrett Estimate of the Standard Error of x, ..... 69 Contents 3.5.4 R and S-PLUS Function m j se .............................. 70 3.5.5 The Harrell-Davis Estimator ............................... 71 3.5.6 R and S-PLUS Function hd ................................. 72 3.5.7 A Bootstrap Estimate of the Standard Error of êq ........... 72 3.5.8 R and S-PLUS Function hdseb ............................. 72 3.6 An M-Estimator of Location ........................................ 73 3.6.1 Computing an M-Estimator of Location .................... 79 3.6.2 R and S-PLUS Function mest .............................. 81 3.6.3 Estimating the Standard Error of the M-Estimator .......... 81 3.6.4 R and S-PLUS Function mestse ............................ 84 3.6.5 A Bootstrap Estimate of the Standard Error of џт .......... 84 3.6.6 R and S-PLUS Function mestseb ........................... 85 3.7 One-Step M-Estimator .............................................. 85 3.7.1 R and S-PLUS Function onestep ........................... 86 3.8 W-Estimators ....................................................... 87 3.9 The Hodges-Lehmann Estimator ................................... 88 3.10 Skipped Estimators ................................................. 88 3.10.1 R and S-PLUS Functions mom and bmean .................... 89 3.11 Some Comparisons of the Location Estimators ...................... 90 3.12 More Measures of Scale ............................................. 92 3.12.1 The Biweight Midvariance ................................. 93 3.12.2 R and S-PLUS Function bivar ............................. 96 3.12.3 The Percentage Bend Midvariance ......................... 96 3.12.4 R and S-PLUS Function pbvar ............................. 98 3.12.5 The Interquartile Range .................................... 98 3.12.6 R and S-PLUS Function ideali ............................ 99 3.13 Some Outlier Detection Methods .................................... 99 3.13.1 Rules Based on Means and Variances ...................... 99 3.13.2 A Method Based on the Interquartile Range ................ 100 3.13.3 Carling s Modification ..................................... 100 3.13.4 A MAD-Median Rule ...................................... 101 3.13.5 R and S-PLUS Functions outbox and out ................... 101 3.14 Exercises ........................................................... 102 W Contents Chapter 4 Confidence Intervals in the One-Sample Case ........... 1 05 4.1 Problems When Working with Means ............................... 105 4.2 The g-and-h Distribution ........................................... 110 4.3 Inferences About the Trimmed Mean ............................... 113 4.3.1 R and S-PLUS Function trimci ............................ 117 4.4 Basic Bootstrap Methods ............................................ 117 4.4.1 The Percentile Bootstrap Method .......................... 118 4.4.2 R and S-PLUS Function onesampb .......................... 119 4.4.3 Bootstrap-t Method ........................................ 119 4.4.4 Bootstrap Methods When Using a Trimmed Mean ......... 121 4.4.5 Singh s Modification ....................................... 125 4.4.6 R and S-PLUS Functions trimpb and trimcibt ............. 126 4.5 Inferences About M-Estimators ..................................... 127 4.5.1 R and S-PLUS Functions městci and momci ................ 129 4.6 Confidence Intervals for Quantiles .................................. 130 4.6.1 · Alteranative Method for the Median ....................... 132 4.6.2 R and S-PLUS Functions qmj ci, hdci, sint, qci, and qint .............................................. 133 4.7 Concluding Remarks ............................................... 134 4.8 Exercises ........................................................... 135 Chapter 5 Comparing Two Groups .................................. 137 5.1 The Shift Function .................................................. 139 5.1.1 The Kolmogorov-Smirnov Test ............................ 142 5.1.2 R and S-PLUS Functions ks, kssig, kswsig, and kstiesig .............................................. 145 5.1.3 The S Band and W Band for the Shift Function ............. 147 5.1.4 R and S-PLUS Functions sband and wband ................. 148 5.1.5 Confidence Band for the Deciles Only ...................... 151 5.1.6 R and S-PLUS Function shifthd ........................... 153 5.1.7 R and S-PLUS Functions g2plot and splotg2 .............. 155 5.2 Student s t Test ..................................................... 155 Contents vii 5.3 The Yuen-Welch Test ............................................... 159 5.3.1 R and S-PLUS Function yuen .............................. 161 5.3.2 A Bootstrap-t Method for Comparing Trimmed Means ..... 162 5.3.3 S-PLUS Function yuenbt ................................... 165 5.4 Inferences Based on a Percentile Bootstrap Method .................. 167 5.4.1 Comparing M-Estimators .................................. 168 5.4.2 Comparing Trimmed Means ............................... 169 5.4.3 R and S-PLUS Functions trimpb2, pb2gen, and m2ci ....... 169 5.5 Comparing Measures of Scale ....................................... 170 5.5.1 Comparing Variances ...................................... 170 5.5.2 R and S-PLUS Function comvar2 ........................... 171 5.5.3 Comparing Biweight Mid variances ........................ 171 5.5.4 R and S-PLUS Function b2ci .............................. 171 5.6 Permutation Tests .................................................. 172 5.6.1 R and S-PLUS Function permg ............................. 173 5.7 Some Heteroscedastic, Rank-Based Methods ........................ 173 5.7.1 R and S-PLUS Function mee ................................ 174 5.7.2 Handling Tied Values ..................................... 176 5.7.3 R and S-PLUS Functions cid and bmp ...................... 180 5.8 Comparing Two Independent Binomials ............................ 181 5.8.1 Storer-Kim Method ....................................... 182 5.8.2 Beal s Method ............................................. 183 5.8.3 R and S-PLUS Functions twobinom and twobici ........... 184 5.9 Comparing Dependent Groups ..................................... 184 5.9.1 Comparing Deciles ........................................ 185 5.9.2 R and S-PLUS Function shif tdhd .......................... 186 5.9.3 Comparing Trimmed Means ............................... 188 5.9.4 R and S-PLUS Function yuend ............................. 190 5.9.5 A Bootstrap-t Method for Marginal Trimmed Means ....... 191 5.9.6 R and S-PLUS Function ydbt .............................. 192 5.9.7 Percennie Bootstrap: Comparing M-Estimators and Other Measures of Location and Scale ............................ 192 5.9.8 R and S-PLUS Function bootdpci .......................... 194 5.9.9 Comparing Variances ...................................... 195 viii Contents 5.9.10 The Sign Test and Inferences About the Binomial Distribution ...................................... 196 5.9.11 R and S-PLUS Function binomci ........................... 198 5.10 Exercises ........................................................... 199 Chapter 6 Some Multivariate Methods .............................. 203 6.1 Generalized Variance ............................................... 203 6.2 Depth .............................................................. 204 6.2.1 Mahalanobis Depth ........................................ 204 6.2.2 Halfspace Depth ........................................... 205 6.2.3 Computing Halfspace Depth .............................. 207 6.2.4 R and S-PLUS Functions depth2, depth, f depth, f depthv2, unidepth, depth2 . for,depth3 . for, f depth . for, f depthv2 . f or, and ufdepth.for ........................... 210 6.2.5 Projection Depth ........................................... 211 6.2.6 R and S-PLUS Functions pdis and pdis. f or ............... 212 6.2.7 Other Measures of Depth .................................. 213 6.2.8 R and S-PLUS Function zdepth ............................ 214 6.3 Some Affine-Equivariant Estimators ................................ 214 6.3.1 Minimum-Volume Ellipsoid Estimator ..................... 215 6.3.2 The Minimum-Covariance Determinant Estimator ......... 216 6.3.3 S-Estimators and Constrained M-Estimators ............... 216 6.3.4 Donoho-Gasko Generalization of a Trimmed Mean ........ 218 6.3.5 R and S-PLUS Functions dmean and dmean .for ............. 219 6.3.6 The Stahel-Donoho W-Estimator .......................... 220 6.4 Multivariate Outlier Detection Methods ............................. 221 6.4.1 A Relplot .................................................. 222 6.4.2 R and S-PLUS Function relplot ........................... 223 6.4.3 TheMVEMethod ......................................... 226 6.4.4 TheMCDMethod ......................................... 226 6.4.5 R and S-PLUS Functions cov . mve and cov . mcd ............. 226 6.4.6 R and S-PLUS Functions outmve and out ................... 227 6.4.7 TheMGVMethod ......................................... 228 6.4.8 R and S-PLUS Function outmgv ............................ 231 Contents /χ 6.4.9 A Projection Method ....................................... 231 6.4.10 R and S-PLUS Functions outpro and outpro . for .......... 233 6.4.11 Comments on Choosing a Method ......................... 234 6.5 A Skipped Estimator of Location and Scatter ........................ 236 6.5.1 R and S-PLUS Functions smean, smean . for, wmcd, wmve, mgvmean, and spat ......................................... 238 6.6 Confidence Region and Inference Based on the OP Estimator of Location ............................................................ 240 6.6.1 R and S-PLUS Functions smeancr and smeancr . for ........ 241 6.6.2 Inferences Based on the MGV Estimator ................... 243 6.6.3 R and S-PLUS Function smgvcr ............................ 244 6.7 Two-Sample Case .................................................. 244 6.7.1 R and S-PLUS Functions smean2 and smean2 .for .......... 245 6.8 Multivariate Density Estimators .................................... 245 6.9 A Two-Sample, Projection-Type Extension of the Wilcoxon-Mann-Whimey Test ..................................... 247 6.9.1 R and S-PLUS Functions mulwmw and mulwmw .for .......... 249 6.10 A Relative Depth Analog of the Wilcoxon-Mann-Whitney Test ..... 250 6.10.1 R and S-PLUS Functions mwmw and mwnw .for ............... 252 6.11 Comparisons Based on Depth ....................................... 253 6.11.1 R and S-PLUS Functions Isqs3, Isqs3.for, and depthg2 ... 256 6.12 Comparing Dependent Groups Based on All Pairwise Differences ... 259 6.12.1 R and S-PLUS Function df ried ............................ 261 6.13 Exercises ........................................................... 262 Chapter 7 One-Way and Higher Designs for Independent Groups ...................................... 265 7.1 Trimmed Means and a One-Way Design ............................ 266 7.1.1 A Welch-Type Adjusted Degrees of Freedom Procedure ... 266 7.1.2 R and S-PLUS Function t iway ............................. 268 7.1.3 A Generalization of Box s Method ......................... 270 7.1.4 R and S-PLUS Function boxlway ........................... 270 7.1.5 Comparing Medians ....................................... 271 Contents 7.1.6 R and S-PLUS Function medlway ........................... 272 7.1.7 A Bootstrap-t Method ..................................... 272 7.1.8 R and S-PLUS Function tlwaybt ........................... 273 7.1.9 Percentile Bootstrap Methods .............................. 275 7.2 Two-Way Designs and Trimmed Means ............................ 275 7.2.1 R and S-PLUS Function t2way ............................. 277 7.2.2 Comparing Medians ....................................... 282 7.2.3 R and S-PLUS Function med2way ........................... 283 7.3 Three-Way Designs and Trimmed Means ........................... 284 7.3.1 R and S-PLUS Function t3way ............................. 286 7.4 Multiple Comparisons Based on Trimmed Means ................... 289 7.4.1 R and S-PLUS Function lincon ............................ 291 7.4.2 Multiple Comparisons and Two-Way Designs ............. 295 7.4.3 R and S-PLUS Functions mcp2atm and mcp^ed ............. 295 7.4.4 A Bootstrap-t Procedure ................................... 296 7.4.5 R and S-PLUS Function linconb ........................... 297 7.4.6 Judging Sample Sizes ...................................... 299 7.4.7 R and S-PLUS Function hochberg .......................... 301 7.4.8 A Percentile Bootstrap Method for Comparing 20% Trimmed Means ........................................... 301 7.4.9 R and S-PLUS Function mcppb20 ........................... 302 7.5 A Random Effects Model for Trimmed Means ....................... 302 7.5.1 A Winsorized Intraclass Correlation ....................... 303 7.5.2 R and S-PLUS Function rananova .......................... 306 7.6 Bootstrap Methods and M-Measures of Location .................... 307 7.6.1 R and S-PLUS Functions blway and pbadepth .............. 310 7.6.2 M-Estimators and Multiple Comparisons .................. 311 7.6.3 R and S-PLUS Functions linconm and pbmcp ............... 315 7.6.4 M-Estimators and the Random Effects Model .............. 315 7.6.5 Other Methods for One-Way Designs ...................... 316 7.7 M-Measures of Location and a Two-Way Design .................... 316 7.7.1 R and S-PLUS Functions pbad2way and mcp2a .............. 318 7.8 Ranked-Based Methods for a One-Way Design ...................... 319 7.8.1 The Rust-Fligner Method .................................. 319 Contents xi 7.8.2 R and S-PLUS Function rf anova........................... 320 7.8.3 A Heteroscedastic Rank-Based Method That Allows Tied Values ................................................ 320 7.8.4 R and S-PLUS Function bdm ................................ 323 7.9 A Rank-Based Method for a Two-Way Design ...................... 324 7.9.1 R and S-PLUS Function bdm2way ........................... 325 7.9.2 The Patel-Hoel Approach to Interactions .................. 325 7.9.3 R and S-PLUS Function rimul ............................. 328 7.10 Exercises ........................................................... 328 Chapter 8 Comparing Multiple Dependent Groups .................. 333 8.1 Comparing Trimmed Means ........................................ 333 8.1.1 Omnibus Test Based on the Trimmed Means oř the Marginal Distributions ................................. 334 8.1.2 R and S-PLUS Function rmanova ........................... 334 8.1.3 Pairwise Comparisons and Linear Contrasts with Trimmed Means ........................................... 337 8.1.4 Linear Contrasts Based on Difference Scores ............... 339 8.1.5 R and S-PLUS Function rmmcp ............................. 340 8.1.6 Judging the Sample Size ................................... 340 8.1.7 RandS-PLUSFunctionssteinl.trandstein2.tr ........ 341 8.2 Bootstrap Methods Based on Marginal Distributions ................ 342 8.2.1 Comparing Trimmed Means ............................... 342 8.2.2 R and S-PLUS Function rmanovab .......................... 343 8.2.3 Multiple Comparisons Based on Trimmed Means .......... 343 8.2.4 R and S-PLUS Functions pairdepb and bptd ............... 345 8.2.5 Percentile Bootstrap Methods .............................. 347 8.2.6 R and S-PLUS Functions bdlway and ddep ................. 348 8.2.7 Multiple Comparisons Using M-Estimators ................ 350 8.2.8 R and S-PLUS Function lindm ............................. 352 8.3 Percentile Bootstrap Methods Based on Difference Scores ........... 353 8.3.1 R and S-PLUS Function rmdzero ........................... 355 8.3.2 Multiple Comparisons ..................................... 355 8.3.3 R and S-PLUS Function rmmcppb ........................... 357 xli Contents 8.4 Comments on Which Method to Use ................................ 358 8.5 Some Rank-Based Methods ......................................... 359 8.5.1 R and S-PLUS Function apanova ........................... 359 8.6 A Split-Plot Design ................................................. 360 8.6.1 A Method Based on Trimmed Means ...................... 361 8.6.2 R and S-PLUS Function tsplit ............................ 362 8.6.3 Bootstrap-t Method ........................................ 365 8.6.4 S-PLUS Function tsplitbt ................................ 366 8.6.5 Using MOMs, Medians, and M-Estimators ................. 366 8.6.6 R and S-PLUS Functions sppba, sppbb, and sppbi .......... 368 8.6.7 A Rank-Based Approach ................................... 369 8.6.8 R and S-PLUS Function bwrank ............................ 372 8.6.9 Rank-Based Multiple Comparisons ........................ 375 8.6.10 R and S-PLUS Function bwrmcp ............................ 375 8.6.11 Multiple Comparisons When Using a Patel-Hoel Approach to Interactions .................................. 375 8.6.12 R and S-PLUS Function sisplit ........................... 377 8.7 Some Rank-Based Multivariate Methods ............................ 377 8.7.1 The Munzel-Brunner Method ............................. 377 8.7.2 R and S-PLUS Function mulrank ........................... 378 8.7.3 The Choi-Marden Multivariate Rank Test ................. 380 8.7.4 S-PLUS Function cmanova ................................. 381 8.8 Exercises ........................................................... 382 Chapter 9 Correlation and Tests of Independence .................. 383 9.1 Problems with the Product Moment Correlation .................... 384 9.1.1 Features of Data That Affect r and Γ ....................... 387 9.1.2 A Heteroscedastic Test of Independence Based on ρ ....... 388 9.2 Two Types of Robust Correlations .................................. 389 9.3 Some Type M Measures of Correlation .............................. 389 9.3.1 The Percentage Bend Correlation .......................... 389 9.3.2 A Test of Independence Based on ррь ...................... 392 9.3.3 R and S-PLUS Function pbcor ............................. 392 Contents xiii 9.3.4 A Test of Zero Correlation Among ρ Random Variables — 393 9.3.5 R and S-PLUS Function pball ............................. 395 9.3.6 The Winsorized Correlation ............................... 396 9.3.7 R and S-PLUS Functions wincor and winall ............... 397 9.3.8 The Biweight Midcovariance ............................... 399 9.3.9 R and S-PLUS Functions bicov and bicovm ................ 400 9.3.10 Kendall s Tau.............................................. 400 9.3.11 Spearman s Rho ........................................... 401 9.3.12 R and S-PLUS Functions tau, spear, and taureg ........... 402 9.3.13 Heteroscedastic Tests of Zero Correlation .................. 402 9.3.14 R and S-PLUS Functions corb and pcorb ................... 403 9.4 Some Type О Correlations .......................................... 404 9.4.1 MVE and MCD Correlations ............................... 404 9.4.2 Skipped Measures of Correlation .......................... 404 9.4.3 The OP Correlation ........................................ 405 9.4.4 Inferences Based on Multiple Skipped Correlations ........ 405 9.4.5 R and S-PLUS Functions scor and mscor ................... 407 9.5 A Test of Independence Sensitive to Curvature or a Linear Association .................................................. 408 9.5.1 R and S-PLUS Functions indt and indtall ................ 410 9.6 Exercises ........................................................... 411 Chapter 1 0 Robust Regression ........................................ 413 10.1 Problems with Ordinary Least Squares .............................. 415 10.1.1 Computing Confidence Intervals Under Heteroscedasticity .................................. 418 10.1.2 An Omnibus Test .......................................... 420 10.1.3 R and S-PLUS Functions lsfitNci and lsfitci ........... 421 10.2 Theil-Sen Estimator ................................................ 423 10.2.1 R and S-PLUS Functions tsreg and correg ................ 426 10.3 Least Median of Squares ............................................ 427 10.3.1 R and S-PLUS Function lmsreg ............................ 427 10.4 Least Trimmed Squares Estimator .................................. 428 10.4.1 R and S-PLUS Functions ltsreg and ltsgreg .............. 428 xiv Contents 10.5 Least Trimmed Absolute Value Estimator ........................... 428 10.5.1 R and S-PLUS Function ltareg ............................ 429 10.6 M-Estimators ....................................................... 429 10.7 The Hat Matrix ..................................................... 431 10.8 Generalized M-Estimators .......................................... 434 10.8.1 R and S-PLUS Function bmreg ............................. 437 10.9 The Coakley-Hettmansperger Estimator ............................ 438 10.9.1 R and S-PLUS Function chreg ............................. 440 10.10 Skipped Estimators ................................................. 441 10.10.1 R and S-PLUS Functions mgvreg, mgvreg . for, opreg, and opreg. f or ............................................ 441 10.11 Deepest Regression Line ............................................ 442 10.11.1 R and S-PLUS Functions depreg and depreg . for .......... 443 10.12 A Criticism of Methods with a High Breakdown Point .............. 443 10.13 Some Additional Estimators ........................................ 443 10.13.1 S-Estimators and τ -Estimators ............................. 444 10.13.2 R and S-PLUS Functions snmreg and stsreg ............... 445 10.13.3 E -Туре Skipped Estimators ................................ 445 10.13.4 R and S-PLUS Functions mbmreg, tstsreg, and gyreg ...... 447 10.13.5 Correlation Methods ....................................... 448 10.13.6 R and S-PLUS Functions bireg and winreg ................ 450 10.13.7 L-Estimators ............................................... 451 10.13.8 L Regression and Quantile Estimation .................... 451 10.13.9 R and S-PLUS Function qreg .............................. 452 10.13.10 Methods Based on Estimates of the Optimal Weights ................................................... 452 10.13.11 Projection Estimators ...................................... 453 10.13.12 Methods Based on Ranks .................................. 454 10.14 Comments About Various Estimators ............................... 455 10.14.1 Contamination Bias ........................................ 457 10.15 Detecting Regression Outliers ....................................... 462 10.15.1 R and S-PLUS Function reglev ............................ 462 10.16 Exercises ........................................................... 464 Contents xv Chapter 11 More Regression Methods ................................ 467 11.1 Inferential Methods Based on Robust Estimators .................... 467 11.1.1 Omnibus Tests for Regression Parameters ................. 467 11.1.2 R and S-PLUS Function regtest........................... 472 11.1.3 Inferences About Individual Parameters ................... 474 11.1.4 R and S-PLUS Function regci ............................. 475 11.1.5 Inferences Based on the OP Estimator ...................... 477 11.1.6 R and S-PLUS Functions opr eg and opregpb. f or .......... 480 11.2 Comparing the Parameters of Two Independent Groups ............ 480 11.2.1 R and S-PLUS Function reg2ci ............................ 483 11.3 Curvature and Half-Slope Ratios .................................... 484 11.3.1 R and S-PLUS Function hratio ............................ 486 11.4 Curvature and Nonparametric Regression .......................... 488 11.4.1 Smoothers. ................................................ 488 11.4.2 The Single-Predictor Case ................................. 489 11.4.3 R and S-PLUS Functions lplot, kerreg, and logrsm ....... 491 11.4.4 The Running-Interval Smoother ........................... 492 11.4.5 R and S-PLUS Functions runmean, rungen, runmbo, and runhat ................................................ 497 11.4.6 Skipped Smoothers ........................................ 500 11.4.7 Smoothing with More Than One Predictor ................. 500 11.4.8 R and S-PLUS Functions runm3d, run3hat, rung3d, run3bo, rung3hat, rplot, and rplotsm ............................. 501 11.4.9 LOESS ..................................................... 505 11.4.10 Generalized Additive Models .............................. 509 11.4.11 R and S-PLUS Functions adrun, adrunl, and gamplot ...... 510 11.5 Checking the Specification of a Regression Model ................... 511 11.5.1 Testing the Hypothesis of a Linear Association ............. 512 11.5.2 R and S-PLUS Function lintest ........................... 513 11.5.3 Testing the Hypothesis of a Generalized Additive Model ... 514 11.5.4 R and S-PLUS Function adtest ............................ 515 11.5.5 Inferences About the Components of a Generalized Additive Model ........................................... 515 11.5.6 R and S-PLUS Function adcom ............................. 516 xvi Contents 11.6 Detecting Interactions .............................................. 517 11.6.1 R and S-PLUS Functions kercon, riplot, and runsm2g ............................................... 519 11.7 Comparing Parametric, Additive, and Nonparametric Fits .......... 520 11.7.1 R and S-PLUS Functions adpchk and pmodchk .............. 520 11.8 ANCOVA .......................................................... 522 11.8.1 R and S-PLUS Functions ancova, ancpb, runmean2g, and ancboot ............................................... 526 11.8.2 Multiple Covariates ....................................... 530 11.8.3 An Alternative Approach .................................. 531 11.8.4 R and S-PLUS Functions ancdes, ancovamp, ancmppb, and ancom ................................................. 532 11.9 Exercises ........................................................... 534 References ............................................................. 537 Index ................................................................... 575
adam_txt	Contents Preface . xvii Chapter I Introduction . I 1.1 Problems with Assuming Normality . 2 1.2 Transformations . 6 1.3 The Influence Curve . 7 1.4 The Central Limit Theorem . 8 1.5 Is the ANOVA F Robust? . 9 1.6 Regression . 10 1.7 More Remarks . 10 1.8 Using the Computer: R and S-PLUS . 11 1.9 Some Data-Managment Issues . 13 1.9.1 Eliminating Missing Values . 17 Chapter 2 A Foundation for Robust Methods . 19 2.1 Basic Tools for Judging Robustness . 20 2.1.1 Qualitative Robustness . 21 2.1.2 Infinitesimal Robustness . 23 2.1.3 Quantitative Robustness . 25 2.2 Some Measures of Location and Their Influence Function . 26 2.2.1 Quantiles . 26 2.2.2 The Winsorized Mean . 27 iii /v Contents 2.2.3 The Trimmed Mean . 29 2.2.4 M-Measures of Location . 30 2.2.5 R-Measures of Location . 33 2.3 Measures of Scale . 33 2.3.1 Mean Deviation from the Mean . 34 2.3.2 Mean Deviation from the Median . 35 2.3.3 Median Absolute Deviation . 35 2.3.4 The (j-Quantile Range . 35 2.3.5 The Winsorized Variance . 36 2.4 Scale-Equivariant M-Measures of Location . 36 2.5 Winsorized Expected Values . 38 Chapter 3 Estimating Measures of Location and Scale . 43 3.1 A Bootstrap Estimate of a Standard Error . 44 3.1.1 R and S-PLUS Function bootse . 46 3.2 Density Estimators . 47 3.2.1 Normal Kernel . 47 3.2.2 Rosenblatt's Shifted Histogram . 48 3.2.3 The Expected Frequency Curve . 48 3.2.4 An Adaptive Kernel Estimator . 49 3.2.5 R and S-PLUS Functions skerd, kerden, kdplot, rdplot, akerd, and splot . 50 3.3 The Sample Trimmed Mean . 56 3.3.1 R and S-PLUS Function tmean . 59 3.3.2 Estimating the Standard Error of the Trimmed Mean . 59 3.3.3 R and S-PLUS Functions win, winvar, and trimse . 64 3.3.4 Estimating the Standard Error of the Sample Median, M . 64 3.3.5 R and S-PLUS Function msmedse . 65 3.4 The Finite-Sample Breakdown Point . 65 3.5 Estimating Quantiles . 66 3.5.1 Estimating the Standard Error of the Sample Quantile . 67 3.5.2 R and S-PLUS Function qse . 69 3.5.3 The Maritz-Jarrett Estimate of the Standard Error of x, . 69 Contents 3.5.4 R and S-PLUS Function m j se . 70 3.5.5 The Harrell-Davis Estimator . 71 3.5.6 R and S-PLUS Function hd . 72 3.5.7 A Bootstrap Estimate of the Standard Error of êq . 72 3.5.8 R and S-PLUS Function hdseb . 72 3.6 An M-Estimator of Location . 73 3.6.1 Computing an M-Estimator of Location . 79 3.6.2 R and S-PLUS Function mest . 81 3.6.3 Estimating the Standard Error of the M-Estimator . 81 3.6.4 R and S-PLUS Function mestse . 84 3.6.5 A Bootstrap Estimate of the Standard Error of џт . 84 3.6.6 R and S-PLUS Function mestseb . 85 3.7 One-Step M-Estimator . 85 3.7.1 R and S-PLUS Function onestep . 86 3.8 W-Estimators . 87 3.9 The Hodges-Lehmann Estimator . 88 3.10 Skipped Estimators . 88 3.10.1 R and S-PLUS Functions mom and bmean . 89 3.11 Some Comparisons of the Location Estimators . 90 3.12 More Measures of Scale . 92 3.12.1 The Biweight Midvariance . 93 3.12.2 R and S-PLUS Function bivar . 96 3.12.3 The Percentage Bend Midvariance . 96 3.12.4 R and S-PLUS Function pbvar . 98 3.12.5 The Interquartile Range . 98 3.12.6 R and S-PLUS Function ideali . 99 3.13 Some Outlier Detection Methods . 99 3.13.1 Rules Based on Means and Variances . 99 3.13.2 A Method Based on the Interquartile Range . 100 3.13.3 Carling's Modification . 100 3.13.4 A MAD-Median Rule . 101 3.13.5 R and S-PLUS Functions outbox and out . 101 3.14 Exercises . 102 W Contents Chapter 4 Confidence Intervals in the One-Sample Case . 1 05 4.1 Problems When Working with Means . 105 4.2 The g-and-h Distribution . 110 4.3 Inferences About the Trimmed Mean . 113 4.3.1 R and S-PLUS Function trimci . 117 4.4 Basic Bootstrap Methods . 117 4.4.1 The Percentile Bootstrap Method . 118 4.4.2 R and S-PLUS Function onesampb . 119 4.4.3 Bootstrap-t Method . 119 4.4.4 Bootstrap Methods When Using a Trimmed Mean . 121 4.4.5 Singh's Modification . 125 4.4.6 R and S-PLUS Functions trimpb and trimcibt . 126 4.5 Inferences About M-Estimators . 127 4.5.1 R and S-PLUS Functions městci and momci . 129 4.6 Confidence Intervals for Quantiles . 130 4.6.1 · Alteranative Method for the Median . 132 4.6.2 R and S-PLUS Functions qmj ci, hdci, sint, qci, and qint . 133 4.7 Concluding Remarks . 134 4.8 Exercises . 135 Chapter 5 Comparing Two Groups . 137 5.1 The Shift Function . 139 5.1.1 The Kolmogorov-Smirnov Test . 142 5.1.2 R and S-PLUS Functions ks, kssig, kswsig, and kstiesig . 145 5.1.3 The S Band and W Band for the Shift Function . 147 5.1.4 R and S-PLUS Functions sband and wband . 148 5.1.5 Confidence Band for the Deciles Only . 151 5.1.6 R and S-PLUS Function shifthd . 153 5.1.7 R and S-PLUS Functions g2plot and splotg2 . 155 5.2 Student's t Test . 155 Contents vii 5.3 The Yuen-Welch Test . 159 5.3.1 R and S-PLUS Function yuen . 161 5.3.2 A Bootstrap-t Method for Comparing Trimmed Means . 162 5.3.3 S-PLUS Function yuenbt . 165 5.4 Inferences Based on a Percentile Bootstrap Method . 167 5.4.1 Comparing M-Estimators . 168 5.4.2 Comparing Trimmed Means . 169 5.4.3 R and S-PLUS Functions trimpb2, pb2gen, and m2ci . 169 5.5 Comparing Measures of Scale . 170 5.5.1 Comparing Variances . 170 5.5.2 R and S-PLUS Function comvar2 . 171 5.5.3 Comparing Biweight Mid variances . 171 5.5.4 R and S-PLUS Function b2ci . 171 5.6 Permutation Tests . 172 5.6.1 R and S-PLUS Function permg . 173 5.7 Some Heteroscedastic, Rank-Based Methods . 173 5.7.1 R and S-PLUS Function mee . 174 5.7.2 Handling Tied Values . 176 5.7.3 R and S-PLUS Functions cid and bmp . 180 5.8 Comparing Two Independent Binomials . 181 5.8.1 Storer-Kim Method . 182 5.8.2 Beal's Method . 183 5.8.3 R and S-PLUS Functions twobinom and twobici . 184 5.9 Comparing Dependent Groups . 184 5.9.1 Comparing Deciles . 185 5.9.2 R and S-PLUS Function shif tdhd . 186 5.9.3 Comparing Trimmed Means . 188 5.9.4 R and S-PLUS Function yuend . 190 5.9.5 A Bootstrap-t Method for Marginal Trimmed Means . 191 5.9.6 R and S-PLUS Function ydbt . 192 5.9.7 Percennie Bootstrap: Comparing M-Estimators and Other Measures of Location and Scale . 192 5.9.8 R and S-PLUS Function bootdpci . 194 5.9.9 Comparing Variances . 195 viii Contents 5.9.10 The Sign Test and Inferences About the Binomial Distribution . 196 5.9.11 R and S-PLUS Function binomci . 198 5.10 Exercises . 199 Chapter 6 Some Multivariate Methods . 203 6.1 Generalized Variance . 203 6.2 Depth . 204 6.2.1 Mahalanobis Depth . 204 6.2.2 Halfspace Depth . 205 6.2.3 Computing Halfspace Depth . 207 6.2.4 R and S-PLUS Functions depth2, depth, f depth, f depthv2, unidepth, depth2 . for,depth3 . for, f depth . for, f depthv2 . f or, and ufdepth.for . 210 6.2.5 Projection Depth . 211 6.2.6 R and S-PLUS Functions pdis and pdis. f or . 212 6.2.7 Other Measures of Depth . 213 6.2.8 R and S-PLUS Function zdepth . 214 6.3 Some Affine-Equivariant Estimators . 214 6.3.1 Minimum-Volume Ellipsoid Estimator . 215 6.3.2 The Minimum-Covariance Determinant Estimator . 216 6.3.3 S-Estimators and Constrained M-Estimators . 216 6.3.4 Donoho-Gasko Generalization of a Trimmed Mean . 218 6.3.5 R and S-PLUS Functions dmean and dmean .for . 219 6.3.6 The Stahel-Donoho W-Estimator . 220 6.4 Multivariate Outlier Detection Methods . 221 6.4.1 A Relplot . 222 6.4.2 R and S-PLUS Function relplot . 223 6.4.3 TheMVEMethod . 226 6.4.4 TheMCDMethod . 226 6.4.5 R and S-PLUS Functions cov . mve and cov . mcd . 226 6.4.6 R and S-PLUS Functions outmve and out . 227 6.4.7 TheMGVMethod . 228 6.4.8 R and S-PLUS Function outmgv . 231 Contents /χ 6.4.9 A Projection Method . 231 6.4.10 R and S-PLUS Functions outpro and outpro . for . 233 6.4.11 Comments on Choosing a Method . 234 6.5 A Skipped Estimator of Location and Scatter . 236 6.5.1 R and S-PLUS Functions smean, smean . for, wmcd, wmve, mgvmean, and spat . 238 6.6 Confidence Region and Inference Based on the OP Estimator of Location . 240 6.6.1 R and S-PLUS Functions smeancr and smeancr . for . 241 6.6.2 Inferences Based on the MGV Estimator . 243 6.6.3 R and S-PLUS Function smgvcr . 244 6.7 Two-Sample Case . 244 6.7.1 R and S-PLUS Functions smean2 and smean2 .for . 245 6.8 Multivariate Density Estimators . 245 6.9 A Two-Sample, Projection-Type Extension of the Wilcoxon-Mann-Whimey Test . 247 6.9.1 R and S-PLUS Functions mulwmw and mulwmw .for . 249 6.10 A Relative Depth Analog of the Wilcoxon-Mann-Whitney Test . 250 6.10.1 R and S-PLUS Functions mwmw and mwnw .for . 252 6.11 Comparisons Based on Depth . 253 6.11.1 R and S-PLUS Functions Isqs3, Isqs3.for, and depthg2 . 256 6.12 Comparing Dependent Groups Based on All Pairwise Differences . 259 6.12.1 R and S-PLUS Function df ried . 261 6.13 Exercises . 262 Chapter 7 One-Way and Higher Designs for Independent Groups . 265 7.1 Trimmed Means and a One-Way Design . 266 7.1.1 A Welch-Type Adjusted Degrees of Freedom Procedure . 266 7.1.2 R and S-PLUS Function t iway . 268 7.1.3 A Generalization of Box's Method . 270 7.1.4 R and S-PLUS Function boxlway . 270 7.1.5 Comparing Medians . 271 Contents 7.1.6 R and S-PLUS Function medlway . 272 7.1.7 A Bootstrap-t Method . 272 7.1.8 R and S-PLUS Function tlwaybt . 273 7.1.9 Percentile Bootstrap Methods . 275 7.2 Two-Way Designs and Trimmed Means . 275 7.2.1 R and S-PLUS Function t2way . 277 7.2.2 Comparing Medians . 282 7.2.3 R and S-PLUS Function med2way . 283 7.3 Three-Way Designs and Trimmed Means . 284 7.3.1 R and S-PLUS Function t3way . 286 7.4 Multiple Comparisons Based on Trimmed Means . 289 7.4.1 R and S-PLUS Function lincon . 291 7.4.2 Multiple Comparisons and Two-Way Designs . 295 7.4.3 R and S-PLUS Functions mcp2atm and mcp^ed . 295 7.4.4 A Bootstrap-t Procedure . 296 7.4.5 R and S-PLUS Function linconb . 297 7.4.6 Judging Sample Sizes . 299 7.4.7 R and S-PLUS Function hochberg . 301 7.4.8 A Percentile Bootstrap Method for Comparing 20% Trimmed Means . 301 7.4.9 R and S-PLUS Function mcppb20 . 302 7.5 A Random Effects Model for Trimmed Means . 302 7.5.1 A Winsorized Intraclass Correlation . 303 7.5.2 R and S-PLUS Function rananova . 306 7.6 Bootstrap Methods and M-Measures of Location . 307 7.6.1 R and S-PLUS Functions blway and pbadepth . 310 7.6.2 M-Estimators and Multiple Comparisons . 311 7.6.3 R and S-PLUS Functions linconm and pbmcp . 315 7.6.4 M-Estimators and the Random Effects Model . 315 7.6.5 Other Methods for One-Way Designs . 316 7.7 M-Measures of Location and a Two-Way Design . 316 7.7.1 R and S-PLUS Functions pbad2way and mcp2a . 318 7.8 Ranked-Based Methods for a One-Way Design . 319 7.8.1 The Rust-Fligner Method . 319 Contents xi 7.8.2 R and S-PLUS Function rf anova. 320 7.8.3 A Heteroscedastic Rank-Based Method That Allows Tied Values . 320 7.8.4 R and S-PLUS Function bdm . 323 7.9 A Rank-Based Method for a Two-Way Design . 324 7.9.1 R and S-PLUS Function bdm2way . 325 7.9.2 The Patel-Hoel Approach to Interactions . 325 7.9.3 R and S-PLUS Function rimul . 328 7.10 Exercises . 328 Chapter 8 Comparing Multiple Dependent Groups . 333 8.1 Comparing Trimmed Means . 333 8.1.1 Omnibus Test Based on the Trimmed Means oř the Marginal Distributions . 334 8.1.2 R and S-PLUS Function rmanova . 334 8.1.3 Pairwise Comparisons and Linear Contrasts with Trimmed Means . 337 8.1.4 Linear Contrasts Based on Difference Scores . 339 8.1.5 R and S-PLUS Function rmmcp . 340 8.1.6 Judging the Sample Size . 340 8.1.7 RandS-PLUSFunctionssteinl.trandstein2.tr . 341 8.2 Bootstrap Methods Based on Marginal Distributions . 342 8.2.1 Comparing Trimmed Means . 342 8.2.2 R and S-PLUS Function rmanovab . 343 8.2.3 Multiple Comparisons Based on Trimmed Means . 343 8.2.4 R and S-PLUS Functions pairdepb and bptd . 345 8.2.5 Percentile Bootstrap Methods . 347 8.2.6 R and S-PLUS Functions bdlway and ddep . 348 8.2.7 Multiple Comparisons Using M-Estimators . 350 8.2.8 R and S-PLUS Function lindm . 352 8.3 Percentile Bootstrap Methods Based on Difference Scores . 353 8.3.1 R and S-PLUS Function rmdzero . 355 8.3.2 Multiple Comparisons . 355 8.3.3 R and S-PLUS Function rmmcppb . 357 xli Contents 8.4 Comments on Which Method to Use . 358 8.5 Some Rank-Based Methods . 359 8.5.1 R and S-PLUS Function apanova . 359 8.6 A Split-Plot Design . 360 8.6.1 A Method Based on Trimmed Means . 361 8.6.2 R and S-PLUS Function tsplit . 362 8.6.3 Bootstrap-t Method . 365 8.6.4 S-PLUS Function tsplitbt . 366 8.6.5 Using MOMs, Medians, and M-Estimators . 366 8.6.6 R and S-PLUS Functions sppba, sppbb, and sppbi . 368 8.6.7 A Rank-Based Approach . 369 8.6.8 R and S-PLUS Function bwrank . 372 8.6.9 Rank-Based Multiple Comparisons . 375 8.6.10 R and S-PLUS Function bwrmcp . 375 8.6.11 Multiple Comparisons When Using a Patel-Hoel Approach to Interactions . 375 8.6.12 R and S-PLUS Function sisplit . 377 8.7 Some Rank-Based Multivariate Methods . 377 8.7.1 The Munzel-Brunner Method . 377 8.7.2 R and S-PLUS Function mulrank . 378 8.7.3 The Choi-Marden Multivariate Rank Test . 380 8.7.4 S-PLUS Function cmanova . 381 8.8 Exercises . 382 Chapter 9 Correlation and Tests of Independence . 383 9.1 Problems with the Product Moment Correlation . 384 9.1.1 Features of Data That Affect r and Γ . 387 9.1.2 A Heteroscedastic Test of Independence Based on ρ . 388 9.2 Two Types of Robust Correlations . 389 9.3 Some Type M Measures of Correlation . 389 9.3.1 The Percentage Bend Correlation . 389 9.3.2 A Test of Independence Based on ррь . 392 9.3.3 R and S-PLUS Function pbcor . 392 Contents xiii 9.3.4 A Test of Zero Correlation Among ρ Random Variables — 393 9.3.5 R and S-PLUS Function pball . 395 9.3.6 The Winsorized Correlation . 396 9.3.7 R and S-PLUS Functions wincor and winall . 397 9.3.8 The Biweight Midcovariance . 399 9.3.9 R and S-PLUS Functions bicov and bicovm . 400 9.3.10 Kendall's Tau. 400 9.3.11 Spearman's Rho . 401 9.3.12 R and S-PLUS Functions tau, spear, and taureg . 402 9.3.13 Heteroscedastic Tests of Zero Correlation . 402 9.3.14 R and S-PLUS Functions corb and pcorb . 403 9.4 Some Type О Correlations . 404 9.4.1 MVE and MCD Correlations . 404 9.4.2 Skipped Measures of Correlation . 404 9.4.3 The OP Correlation . 405 9.4.4 Inferences Based on Multiple Skipped Correlations . 405 9.4.5 R and S-PLUS Functions scor and mscor . 407 9.5 A Test of Independence Sensitive to Curvature or a Linear Association . 408 9.5.1 R and S-PLUS Functions indt and indtall . 410 9.6 Exercises . 411 Chapter 1 0 Robust Regression . 413 10.1 Problems with Ordinary Least Squares . 415 10.1.1 Computing Confidence Intervals Under Heteroscedasticity . 418 10.1.2 An Omnibus Test . 420 10.1.3 R and S-PLUS Functions lsfitNci and lsfitci . 421 10.2 Theil-Sen Estimator . 423 10.2.1 R and S-PLUS Functions tsreg and correg . 426 10.3 Least Median of Squares . 427 10.3.1 R and S-PLUS Function lmsreg . 427 10.4 Least Trimmed Squares Estimator . 428 10.4.1 R and S-PLUS Functions ltsreg and ltsgreg . 428 xiv Contents 10.5 Least Trimmed Absolute Value Estimator . 428 10.5.1 R and S-PLUS Function ltareg . 429 10.6 M-Estimators . 429 10.7 The Hat Matrix . 431 10.8 Generalized M-Estimators . 434 10.8.1 R and S-PLUS Function bmreg . 437 10.9 The Coakley-Hettmansperger Estimator . 438 10.9.1 R and S-PLUS Function chreg . 440 10.10 Skipped Estimators . 441 10.10.1 R and S-PLUS Functions mgvreg, mgvreg . for, opreg, and opreg. f or . 441 10.11 Deepest Regression Line . 442 10.11.1 R and S-PLUS Functions depreg and depreg . for . 443 10.12 A Criticism of Methods with a High Breakdown Point . 443 10.13 Some Additional Estimators . 443 10.13.1 S-Estimators and τ -Estimators . 444 10.13.2 R and S-PLUS Functions snmreg and stsreg . 445 10.13.3 E -Туре Skipped Estimators . 445 10.13.4 R and S-PLUS Functions mbmreg, tstsreg, and gyreg . 447 10.13.5 Correlation Methods . 448 10.13.6 R and S-PLUS Functions bireg and winreg . 450 10.13.7 L-Estimators . 451 10.13.8 L\ Regression and Quantile Estimation . 451 10.13.9 R and S-PLUS Function qreg . 452 10.13.10 Methods Based on Estimates of the Optimal Weights . 452 10.13.11 Projection Estimators . 453 10.13.12 Methods Based on Ranks . 454 10.14 Comments About Various Estimators . 455 10.14.1 Contamination Bias . 457 10.15 Detecting Regression Outliers . 462 10.15.1 R and S-PLUS Function reglev . 462 10.16 Exercises . 464 Contents xv Chapter 11 More Regression Methods . 467 11.1 Inferential Methods Based on Robust Estimators . 467 11.1.1 Omnibus Tests for Regression Parameters . 467 11.1.2 R and S-PLUS Function regtest. 472 11.1.3 Inferences About Individual Parameters . 474 11.1.4 R and S-PLUS Function regci . 475 11.1.5 Inferences Based on the OP Estimator . 477 11.1.6 R and S-PLUS Functions opr eg and opregpb. f or . 480 11.2 Comparing the Parameters of Two Independent Groups . 480 11.2.1 R and S-PLUS Function reg2ci . 483 11.3 Curvature and Half-Slope Ratios . 484 11.3.1 R and S-PLUS Function hratio . 486 11.4 Curvature and Nonparametric Regression . 488 11.4.1 Smoothers. . 488 11.4.2 The Single-Predictor Case . 489 11.4.3 R and S-PLUS Functions lplot, kerreg, and logrsm . 491 11.4.4 The Running-Interval Smoother . 492 11.4.5 R and S-PLUS Functions runmean, rungen, runmbo, and runhat . 497 11.4.6 Skipped Smoothers . 500 11.4.7 Smoothing with More Than One Predictor . 500 11.4.8 R and S-PLUS Functions runm3d, run3hat, rung3d, run3bo, rung3hat, rplot, and rplotsm . 501 11.4.9 LOESS . 505 11.4.10 Generalized Additive Models . 509 11.4.11 R and S-PLUS Functions adrun, adrunl, and gamplot . 510 11.5 Checking the Specification of a Regression Model . 511 11.5.1 Testing the Hypothesis of a Linear Association . 512 11.5.2 R and S-PLUS Function lintest . 513 11.5.3 Testing the Hypothesis of a Generalized Additive Model . 514 11.5.4 R and S-PLUS Function adtest . 515 11.5.5 Inferences About the Components of a Generalized Additive Model . 515 11.5.6 R and S-PLUS Function adcom . 516 xvi Contents 11.6 Detecting Interactions . 517 11.6.1 R and S-PLUS Functions kercon, riplot, and runsm2g . 519 11.7 Comparing Parametric, Additive, and Nonparametric Fits . 520 11.7.1 R and S-PLUS Functions adpchk and pmodchk . 520 11.8 ANCOVA . 522 11.8.1 R and S-PLUS Functions ancova, ancpb, runmean2g, and ancboot . 526 11.8.2 Multiple Covariates . 530 11.8.3 An Alternative Approach . 531 11.8.4 R and S-PLUS Functions ancdes, ancovamp, ancmppb, and ancom . 532 11.9 Exercises . 534 References . 537 Index . 575
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spelling	Wilcox, Rand R. Verfasser (DE-588)141426241 aut Introduction to robust estimation and hypothesis testing Rand R. Wilcox Robust estimation and hypothesis testing 2. ed. Amsterdam [u.a.] Elsevier Acad. Press 2005 XIX, 588 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Robuustheid gtt Schattingstheorie gtt Statistische toetsen gtt Estimation theory Robust statistics Statistical hypothesis testing Robuste Schätzung (DE-588)4178265-3 gnd rswk-swf Statistischer Test (DE-588)4077852-6 gnd rswk-swf Statistischer Test (DE-588)4077852-6 s DE-604 Robuste Schätzung (DE-588)4178265-3 s Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016297193&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Wilcox, Rand R. Introduction to robust estimation and hypothesis testing Robuustheid gtt Schattingstheorie gtt Statistische toetsen gtt Estimation theory Robust statistics Statistical hypothesis testing Robuste Schätzung (DE-588)4178265-3 gnd Statistischer Test (DE-588)4077852-6 gnd
subject_GND	(DE-588)4178265-3 (DE-588)4077852-6
title	Introduction to robust estimation and hypothesis testing
title_alt	Robust estimation and hypothesis testing
title_auth	Introduction to robust estimation and hypothesis testing
title_exact_search	Introduction to robust estimation and hypothesis testing
title_exact_search_txtP	Introduction to robust estimation and hypothesis testing
title_full	Introduction to robust estimation and hypothesis testing Rand R. Wilcox
title_fullStr	Introduction to robust estimation and hypothesis testing Rand R. Wilcox
title_full_unstemmed	Introduction to robust estimation and hypothesis testing Rand R. Wilcox
title_short	Introduction to robust estimation and hypothesis testing
title_sort	introduction to robust estimation and hypothesis testing
topic	Robuustheid gtt Schattingstheorie gtt Statistische toetsen gtt Estimation theory Robust statistics Statistical hypothesis testing Robuste Schätzung (DE-588)4178265-3 gnd Statistischer Test (DE-588)4077852-6 gnd
topic_facet	Robuustheid Schattingstheorie Statistische toetsen Estimation theory Robust statistics Statistical hypothesis testing Robuste Schätzung Statistischer Test
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016297193&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT wilcoxrandr introductiontorobustestimationandhypothesistesting AT wilcoxrandr robustestimationandhypothesistesting

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