Holdings: Introduction to robust estimation and hypothesis testing

Introduction to robust estimation and hypothesis testing:

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Bibliographic Details
Main Author:	Wilcox, Rand R. (Author)
Format:	Book
Language:	English
Published:	Amsterdam [u.a.] Elsevier, AP 2012
Edition:	3. ed.
Subjects:	Robuste Schätzung Statistischer Test
Online Access:	Inhaltsverzeichnis
Physical Description:	XXI, 690 S. graph. Darst.
ISBN:	9780123869838

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245	1	0	\|a Introduction to robust estimation and hypothesis testing \|c Rand Wilcox
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adam_text	Contents Preface .............................................................................xix Chapter 1 Introduction ...............................................................7 I . I Problems with Assuming Normality ......................................... I 1 .2 Transformations ...............................................................5 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 ............................................................... 11 1.8 Using the Computer: R ...................................................... 11 1.9 Some Data Management Issues ............................................. 13 1.9.1 Eliminating Missing Values ......................................... 22 Chapter 2 A Foundation for Robust Methods ......................................23 2.1 Basic Tools for Judging Robustness ........................................23 2.1 Л Qualitative Robustness .............................................. 24 2.1.2 Infinitesimal Robustness ............................................. 27 2.1.3 Quantitative Robustness ............................................. 28 2.2 Some Measures of Location and Their Influence Function ...............29 2.2.1 Quantiles ............................................................. 29 2.2.2 The Winsorized Mean ............................................... 30 2.2.3 The Trimmed Mean .................................................. 32 2.2.4 M-Measures of Location ............................................ 32 2.2.5 R-Measures of Location ............................................. 35 2.3 Measures of Scale ...........................................................36 2.4 Scale Equivariant M-Measures of Location ................................38 2.5 Winsorized Expected Values ................................................39 Chapter 3 Estimating Measures of Location and Scale .............................43 3.1 A Bootstrap Estimate of a Standard Error ..................................43 3.1.1 R Function bootse ....................................................45 СояїшяН ............46 3.2 Density Estimators ............................................ 3.2.1 Normal Kernel ....................................................... 3.2.2 Rosenblatt s Shifted Histogram ..................................... ąJ 3.2.3 The Expected Frequency Curve ..................................... 47 3.2.4 An Adaptive Kernel Estimator ...................................... 48 3.2.5 R Functions skerd, kerden, kdplot, rdplot, akerd, and splot .......49 3.3 The Sample Trimmed Mean ................................................ 4 3.3. 1 R Functions mean, tmean, and Hoc ................................. 57 3.3.2 Estimating the Standard Error of the Trimmed Mean .............. 57 3.3.3 Estimating the Standard Error of the Sample Winsorized Mean .. 62 3.3.4 R Functions winmean, winvar, trimse, and winse ..................62 3.3.5 Estimating the Standard Error of the Sample Median, M ..........62 3.3.6 R Function msmedse ................................................63 3.4 The Finite Sample Breakdown Point .......................................63 3.5 Estimating Quantiles ........................................................64 3.5. 1 Estimating the Standard Error of the Sample Quantile ............65 3.5.2 R Function qse .......................................................66 3.5.3 The Maritz-Jarrett Estimate of the Standard Error of xq ..........67 3.5.4 R Function mjse ......................................................68 3.5.5 The Harrell-Davis Estimator ........................................68 3.5.6 R Function hd ........................................................69 3.5.7 A Bootstrap Estimate of the Standard Error of Bą ..................69 3.5.8 R Function hdseb .................................................... 70 3.6 An M-Estimator of Location ................................................70 3.6. 1 R Function mad ...................................................... 75 3.6.2 Computing an M-estimator of Location ............................75 3.6.3 R Functions mest ....................................................77 3.6.4 Estimating the Standard Error of the M-estimator ................. 78 3.6.5 R Function mestse ................................................... 80 3.6.6 A Bootstrap Estimate of the Standard Error of џт ................. 80 3.6.7 R Function mestseb .................................................. 81 3.7 One-Step M-estimator .................................. §2 3.7.1 R Function onestep ............................ g3 3.8 W-estimators ...................................... g3 3.8. 1 Tau Measure of Location .................... g4 3.8.2 R Function tauloc ........................ ......... 3.8.3 Zuołs Weighted Estimator ..................... ^ .................... ^ 3.9 The Hodges-Lehmann Estimator .................. .............. g5 3.10 Skipped Estimators ............................ g5 3.10.1 R Functions mom and bmean .............. .................... 3.11 Some Comparisons of the Location Estimators...^.......... ..............86 Contents 3.12 More Measures of Scale .....................................................89 3.12.1 The Biweight Midvariance .......................................... 90 3.12.2 R Function bivar ..................................................... 92 3.12.3 The Percentage Bend Midvariance and tau Measure of Variation ..............................................................92 3.12.4 R Functions pbvar, tauvar ........................................... 94 3.12.5 The Interquartile Range ............................................. 95 3.12.6 R Function idealf .................................................... 96 3.13 Some Outlier Detection Methods ........................................... 96 3.13.1 Rules Based on Means and Variances ..............................96 3.13.2 A Method Based on the Interquartile Range .......................96 3.13.3 Carling s Modification ...............................................97 3.13.4 A MAD-Median Rule ............................................... 97 3.13.5 R Functions outbox, out, and boxplot ...............................98 3.13.6 Skewness and the Boxplot Rule .....................................99 3.13.7 R Function adjboxout ...............................................100 3.14 Exercises ....................................................................100 Chapter 4 Confidence Intervals in the One-Sample Case ...........................103 4. 1 Problems when Working with Means ..................................... 1 03 4.2 The g-and-h Distribution ...................................................107 4.2.1 R Functions ghdist and rmul .......................................110 4.3 Inferences About the Trimmed and Winsorized Means .................. Ill 4.3.1 R Functions trimci and winci ....................................... 114 4.4 Basic Bootstrap Methods ...................................................115 4.4.1 The Percentile Bootstrap Method ..................................115 4.4.2 R Function onesampb ............................................... 116 4.4.3 Bootstrap-t Method ................................................. 117 4.4.4 Bootstrap Methods when Using a Trimmed Mean ................ 118 4.4.5 Singh s Modification ................................................123 4.4.6 R Functions trimpb and trimcibt ...................................123 4.5 Inferences About M-Estimators ...........................................124 4.5.1 R Functions městci and momci ....................................126 4.6 Confidence Intervals for Quantiles ........................................126 4.6.1 Beware of Tied Values when Using the Median ..................129 4.6.2 Alternative Method for the Median ................................130 4.6.3 R Functions qmjci, hdci, sint, sintv2. qci, and qint ................131 4.7 Empirical Likelihood .......................................................132 4.7.1 Bartlett Corrected Empirical Likelihood ..........................133 4.8 Concluding Remarks .......................................................135 4.9 Exercises ....................................................................135 VII Contents 137 Chapter 5 Comparing Two Croups ........................................******* 5.I The Shift Function e Shift Function .......................................................... . 1 The Kol mogorov-S mirno v Test ................................... 141 .2 R Functions ks, kssig, kswsig, and kstiesig ........................144 .3 The S Band and W Band for the Shift Function ...................146 .4 R Functions sband and wband ..................................... !47 .5 Confidence Band for the Deciles Only ............................150 .6 R Function shifthd .................................................. 151 .7 R Functions g2plot and splotg2 ....................................153 153 5. 5. 5. 5. 5. 5. 5. 5.2 Student s f-test 5.3 Comparing Medians and Other Trimmed Means .........................157 5.3.1 R Function yuen ....................................................160 5.3.2 A Bootstrap-t Method for Comparing Trimmed Means ..........161 5.3.3 R Functions yuenbt and yhbt .......................................163 5.3.4 Measuring Effect Size: Robust Analogs of Cohen s d ............166 5.3.5 R Functions akp.effect, yuenv2, and ees.ci ........................169 5.3.6 Comments on Measuring Effect Size ..............................170 5.4 Inferences Based on a Percenti le Bootstrap Method ......................170 5.4.1 Comparing M-Estimators ..........................................171 5.4.2 Comparing Trimmed Means and Medians ........................172 5.4.3 R Functions trimpb2, pb2gen, m2ci, and medpb2 ................173 5.5 Comparing Measures of Scale .............................................174 5.5. 1 Comparing Variances ...............................................174 5.5.2 R Function comvar2 ................................................175 5.5.3 Comparing Biweight Midvariances ................................176 5.5.4 R Function b2ci ..................................................... 176 5.6 Permutation Tests .................................. 176 5.6.1 R Function permg ............................ 177 5.7 Inferences About a Probabilistic Measure of Effect Size .................177 5.7.1 R Function mee ....................... 179 5.7.2 The Cliff and Bruner-Munzel Methods: Handling Tied Values ľ 180 5.7.3 R Functions cid, cidv2, bmp, and wmwloc ........................184 5.8 Comparing Two Independent Binomials ............. . ľ , 186 5.8.1 Storer-Kim Method ....... .................... io7 5.8.2 BeaľsMethod ..... * ........................... ÍL 5.8.3 кмѕ Method .............. u!!! .!!!!!! .............................. [Il 5.8.4 R Functions twobinom, twobici, bi2KMS, bi2KMSv2, an d ...... ................................ 5.8.5 Comparing Discrete Distributions: R Functions binb and ........... anddisc2com ....................... vin Contents 5.9 Comparing Dependent Groups .............................................190 5.9.1 A Shift Function for Dependent Groups ...........................190 5.9.2 R Function lband ....................................................192 5.9.3 Comparing Deciles .................................................192 5.9.4 R Function shiftdhd .................................................193 5.9.5 Comparing Trimmed Means .......................................195 5.9.6 R Functions y uend and yuendv2 ...................................197 5.9.7 A Bootstrap-t Method for Marginal Trimmed Means .............198 5.9.8 R Function ydbt .....................................................198 5.9.9 Inferences about the Distribution of Difference Scores ...........199 5.9.10 R Functions Ioc2dif and I2drmci ...................................200 5.9.11 Percentile Bootstrap: Comparing Medians, M-Estimators and Other Measures of Location and Scale ........................201 5.9.12 R Function bootdpci ................................................202 5.9.13 Handling Missing Values ...........................................203 5.9.14 R Functions rm2miss and rmmismcp ..............................207 5.9.15 Comparing Variances ...............................................208 5.9.16 The Sign Test and Inferences about the Binomial Distribution ... 208 5.9.17 R Functions binomci and acbinomci ...............................211 5.10 Exercises ....................................................................212 Chapter 6 Some Multivariate Methods ............................................215 6. 1 Generalized Variance .......................................................2 1 5 6.2 Depth ........................................................................216 6.2.1 Mahalanobis Depth .................................................216 6.2.2 Halfspace Depth ....................................................216 6.2.3 Computing Halfspace Depth .......................................218 6.2.4 R Functions depth2, depth, fdepth, fdepthv2, and unidepth ......221 6.2.5 Projection Depth ....................................................222 6.2.6 R functions pdis and pdisMC ......................................223 6.2.7 Other Measures of Depth ...........................................223 6.2.8 R Function zdepth ..................................................224 6.3 Some Affine Equivariant Estimators ......................................224 6.3.1 Minimum Volume Ellipsoid Estimator ............................225 6.3.2 The Minimum Covariance Determinant Estimator ...............226 6.3.3 S-Estimators and Constrained M-Estimators ......................227 6.3.4 R Function tbs .......................................................228 6.3.5 Donoho-Gasko Generalization of a Trimmed Mean ..............228 6.3.6 R Functions dmean and dcov .......................................229 6.3.7 The Stahel-Donoho W-Estimator ..................................230 IX Contents ..................231 6.3.8 R Function sdwe ............................... 231 6.3.9 Median Ball Algorithm ............................................. ^ 6.3.10 R Function rmba .................................................... 6.3.11 OGK Estimator ..................................................... 6.3. 1 2 R Function ogk ...................................................... 6.3.13 An M -Estimator ..................................................... 6.3.14 R Function MARest ................................................ 234 6.4 Multivariate Outlier Detection Methods ..................................235 6.4.1 ARelplot ............................................................ 236 6.4.2 R Function relplot ................................................... 23δ 6.4.3 The MVE Method .................................................. 239 6.4.4 The MCD Method ..................................................239 6.4.5 R Functions covmve andcovmcd ..................................239 6.4.6 R function out .......................................................240 6.4.7 The MGV Method ..................................................241 6.4.8 R Function outmgv .................................................243 6.4.9 A Projection Method ...............................................244 6.4.10 R functions outpro and out3d ......................................246 6.4.11 Outlier Identification in High Dimensions .........................247 6.4. 1 2 R Function outproad and outmgvad ...............................247 6.4. 1 3 Approaches Based on Geometric Quantiles .......................248 6.4.14 Comments on Choosing a Method .................................248 6.5 A Skipped Estimator of Location and Scatter .............................250 6.5.1 R Functions smean, wmcd, wmve, mgvmean, Llmedcen, spat, mgvcov, skip, skipcov, and dcov .............................252 6.6 Robust Generalized Variance ..............................................254 6.6.1 R Function gvarg ................................... 255 6.7 Inference in the One-Sample Case ............................. 255 6.7.1 Inferences Based on the OP Measure of Location ................255 6.7.2 Extension of Hotelling s T2 to Trimmed Means ..................256 6.7.3 R Functions smeancrv2 and hotell.tr ............... 257 6.7.4 Inferences Based on the MGV Estimator ..........................259 6.7.5 R Function smg ver ...................... 259 6.8 Two-Sample Case ............................... 259 6.8.1 R Functionssmean2, smean2v2, matsplit, and mat2grp .....ľ... 260 6.8.2 Comparing Robust Generalized Variances ................262 6.8.3 R function gvar2g .................... ........... 6.9 Multivariate Density Estimators ............... .....................262 6.10 A Two-Sample, Projection-Type Extension of the * ^ ^ Wilcoxon-Mann-Whitney Test .................. 263 6.10.1 R fonctions mul wmw and mulwmwv2 ......... ľ. ........ .......265 Contents 6.11 A Relative Depth Analog of the Wilcoxon-Mann-Whitney Test ........267 6. 1 1.1 R function mwmw ..................................................268 6.12 Comparisons Based on Depth ..............................................269 6.12.1 R Functions Isqs3 and depthg2 .....................................272 6.13 Comparing Dependent Groups Based on All Pairwise Differences ......275 6.13.1 R Function dfried ...................................................277 6.14 Robust Principal Components Analysis ...................................277 6.14.1 R Functions prcomp and regpca ...................................279 6.14.2 Maronna s Method ..................................................279 6.14.3 The SPCA Method ..................................................280 6.14.4 Method HRVB ......................................................280 6.14.5 Method OP ..........................................................281 6.14.6 Method PPCA .......................................................281 6.14.7 R Functions outpca, robpca, robpcaS, SPCA, Ppca, and Ppca.summary .......................................................282 6.14.8 Comments on Choosing the Number of Components .............283 6.15 Cluster Analysis ............................................................287 6.15.1 R Functions Kmeans, kmeans.grp, TKmeans, and TKmeans.grp ........................................................288 6.16 Exercises ....................................................................288 Chapter 7 One-Way and Higher Designs for Independent Groups .................291 7. 1 Trimmed Means and a One-Way Design ..................................292 7. 1 . 1 A Welch-Type Procedure and a Robust Measure of Effect Size. . 293 7. 1 .2 R Functions 1 1 way, 1 1 way v2, esmcp, fac2list, and 1 1 wayF .......295 7. 1 .3 A Generalization of Box s Method ................................298 7. 1 .4 R Function box I way ................................................299 7. 1 .5 Comparing Medians ................................................300 7.1.6 R Function med 1 way ...............................................301 7.1.7 A Bootstrap-t method ...............................................301 7.1.8 R Functions 1 1 waybt and btrim ....................................302 7.1.9 Percentile Bootstrap Methods ......................................304 7.2 Two-Way Designs and Trimmed Means ..................................304 7.2. 1 R Functions t2way ..................................................308 7.2.2 Comparing Medians ................................................310 7.2.3 R Function med2way ...............................................311 7.3 Three-Way Designs and Trimmed Means .................................311 7.3.1 R Functions t3way and fac2list ....................................313 7.4 Multiple Comparisons Based on Medians and Other Trimmed Means ..316 7.4.1 An Extension of Yuen s Method to Trimmed Means .............317 7.4.2 R Function lincon ...................................................319 xi Contants 7.4.3 Multiple Comparisons for Two-way and Three-Way _ ..............·.........··.· ÒLL Designs ..................................... 7.4.4 R Functions mcp2atm, mcp2med, mcp3atm, mcp3med, соп2 way, and сопЗ way ............................................ 7.4.5 A Bootstrap-t Procedure ............................................ 325 7.4.6 R Functions linconb, bbtrim, and bbbtrim .........................327 7.4.7 Percentik Bootstrap Methods for Comparing Medians and Other Trimmed Means .............................................. 329 7.4.8 R Functions tmcppb, bbmcppb, bbbmcppb, medpb, med2mcp, med3mcp, and mcppb20 ................................331 7.4.9 Judging Sample Sizes ...............................................333 7.4.10 R Function hochberg ................................................334 7.4.1 1 Explanatory Measure of Effect Size ...............................335 7.4.12 R Functions ESmainMCP andeslmcp .............................335 7.5 A Random Effects Model for Trimmed Means ...........................336 7.5.1 A Winsorized Intraclass Correlation ...............................338 7.5.2 R Function rananova ................................................339 7.6 Global Tests Based on M-Measures of Location .........................340 7.6.1 R Functions b 1 way and pbadepth ..................................343 7.6.2 M-estimators and Multiple Comparisons ..........................344 7.6.3 R Functions linconm and pbmcp ...................................347 7.6.4 M-Estimators and the Random Effects Model ....................348 7.6.5 Other Methods for One-Way Designs .............................348 7.7 M-Measures of Location and a Two-Way Design ........................348 7.7. 1 R Functions pbad2way and mcp2a .................................351 7.8 Ranked-Based Methods for a One-Way Design ..........................351 7.8.1 The Rust-Fligner Method .............................. 352 7.8.2 R Function rfanova ..................... 353 7.8.3 A Heteroscedastic Rank-Based Method that Allows Tied Values .......................... 354 7.8.4 RFunctionbdm ...................... .....................354 7.8.5 Inferences about a Probabilistic Measure of Effect Size . . . ! . 356 7.8.6 R Functions cidmulv2, wmwaov and cidM 358 7.9 A Rank-Based Method for a Two-Way Design... ...................359 7.9.1 R Function bdm2way ............. ........................351 7.9.2 The Patel-Hoel Approach to interactions ...... . . . . . sei 7.9.3 R Function rimu I ...... ..................... ~¿2 7.10 MÁNOVA Based on Trimmed Means .............. ........................ З6З 7.10.1 R Functions MULtr.anova, MULAOVn bw2Hsť and .............. YYmanova ....... r 7.10.2 Linear Contrasts . .......................................... ,1 ................................................367 Xii Contents 7.10.3 R Functions linconMpb, linconSpb, YYmcp, fac2Mlist, and fac2BBMlist ....................................................369 7.1 1 Nested Designs .............................................................371 7.11.1 R Functions anova.nestA, mcp.nestA, and anova.nestAP ........374 7.12 Exercises ....................................................................374 Chapter 8 Comparing Multiple Dependent Croups ................................379 8.1 Comparing Trimmed Means ...............................................379 8.1.1 Omnibus Test Based on the Trimmed Means of the Marginal Distributions ..............................................380 8.1.2 R Function rmanova ................................................380 8.1.3 Pairwise Comparisons and Linear Contrasts Based on Trimmed Means .....................................................381 8.1.4 Linear Contrasts Based on the Marginal Random Variables ......384 8.1.5 R Function rmmcp and rmmismcp .................................385 8.1.6 Judging the Sample Size ............................................386 8.1.7 R Functions stein 1 .tr and stein2.tr .................................387 8.2 Bootstrap Methods Based on Marginal Distributions ....................387 8.2.1 Comparing Trimmed Means .......................................387 8.2.2 R Function rmanovab ...............................................388 8.2.3 Multiple Comparisons Based on Trimmed Means ................388 8.2.4 R Functions pairdepb and bptd .....................................390 8.2.5 Percentile Bootstrap Methods ......................................392 8.2.6 R Functions bdlway and ddep .....................................394 8.2.7 Multiple Comparisons Using M-estimators or Skipped Estimators ...........................................................395 8.2.8 R Functions lindm and mcpOV ....................................397 8.3 Bootstrap Methods Based on Difference Scores ..........................398 8.3.1 R Function rmdzero .................................................400 8.3.2 Multiple Comparisons ..............................................400 8.3.3 R Functions rmmcppb, wmcppb, dmedpb, and lindepbt ..........402 8.4 Comments on which Method to Use ......................................404 8.5 Some Rank-Based Methods ................................................406 8.5.1 R Functions apanova and bprm ....................................408 8.6 Between-by-Within and Within-by-Within Designs ......................408 8.6.1 Analyzing a Between-by-Within Design Based on Trimmed Means .....................................................408 8.6.2 R Functions bwtrim and tsplit ......................................410 8.6.3 Data Management: R Function bw21ist ............................412 8.6.4 Bootstrap-t Method for a Between-by-Within Design ............413 8.6.5 R Functions bwtrimbt and tsplitbt .................................414 xiii Contents 8 6 6 Percentile Bootstrap Methods for a Between-by-Within Design ...............................................................414 8.6.7 R Functions sppba, sppbb, and sppbi .............................. 41 8.6.8 Multiple Comparisons .............................................. 4 ! 8 8.6.9 R Functions bwmcp, bwamcp, bwbmcp, bwimcp, spmcpa, spmcpb, and spmcpi .................................................421 8.6.10 Within-by-Within Designs ......................................... 422 8.6. 1 1 R Functions wwtrim, wwtrimbt, wwmcppb, and wwmcpbt ......423 8.6. 1 2 A Rank-Based Approach ...........................................423 8.6.13 R Function bwrank .................................................427 8.6.14 Rank-Based Multiple Comparisons ................................429 8.6.15 R Function bwrmcp .................................................429 8.6.16 Multiple Comparisons when Using a Patel-Hoel Approach to Interactions .......................................................429 8.6.17 R Function sisplit ...................................................431 8.7 Some Rank-Based Multivariate Methods .................................431 8.7.1 The Munzel-Brunner Method ......................................431 8.7.2 R Function mulrank .................................................433 8.7.3 The Choi-Marden Multivariate Rank Test ........................434 8.7.4 R Function cmanova ................................................435 8.8 Three-Way Designs ........................................................436 8.8.1 Global Tests Based on Trimmed Means ...........................436 8.8.2 R Functions bbwtrim, bwwtrim, wwwtrim, bbwtrimbt, bwwtrimbt, and wwwtrimbt ........................................437 8.8.3 Data Management: R Functions bw21ist and bbw21ist ............437 8.8.4 Multiple Comparisons ..............................................438 8.8.5 R Function гтЗтср .................................................439 8.8.6 R Functions bbwmcp, bwwmcp, bbwmcppb, bwwmcppb, and wwwmcppb ............................................ 439 8.9 Exercises ....................................................... 440 OmpUr9 Correlation and Tests of Independence .................................441 9. 1 Problems with the Product Moment Correlation .......................... 44I 9. 1.1 Features of Data that Affect r and Γ .......................... 444 9. 1. 2 Heteroscedasticity and the Classic Test that ρ = 0............... 445 9.2 Two Types of Robust Correlations ........................................ 446 9.3 Some Type M-Measures of Correlation .................. !.ľ.ľ. ..ľ, ľ. І446 9.3. 1 The Percentage Bend Correlation ....................... 446 9.3.2 A Test of Independence Based on ppb ...............* 447 9.3.3 R Functionpbcor ................................................... 9.3.4 A Test of Zero Correlation among p Random Variables .....! .... . 449 XIV Contents 9.3.5 R Function pball....................................................451 9.3.6 The Winsorized Correlation ........................................452 9.3.7 R Functions wincor and winall .....................................453 9.3.8 The Biweight Midcovariance ......................................454 9.3.9 R Functions bicov and bicovm .....................................455 9.3.10 Kendall s tau........................................................456 9.3.11 Spearman s rho ......................................................457 9.3.12 R Functions tau, spear, cor, and taureg ............................457 9.3.13 Heteroscedastic Tests of Zero Correlation .........................458 9.3.14 R Functions corb, pcorb, and pcorhc4 .............................459 9.4 Some Type О Correlations .................................................460 9.4.1 MVE and MCD Correlations .......................................460 9.4.2 Skipped Measures of Correlation ..................................460 9.4.3 The OP Correlation .................................................461 9.4.4 Inferences Based on Multiple Skipped Correlations ..............461 9.4.5 R Functions scor and mscor ........................................463 9.5 A Test of Independence Sensitive to Curvature ...........................464 9.5.1 R Functions indt, indtall, and medind ..............................466 9.6 Comparing Correlations: Independent Case ..............................467 9.6.1 Comparing Pearson Correlations ...................................467 9.6.2 Comparing Robust Correlations ...................................468 9.6.3 R Functions twopcor and twocor ...................................468 9.7 Exercises ....................................................................468 Chapter 10 Robust Regression ....................................................471 10. 1 Problems with Ordinary Least Squares ....................................472 1 0. 1 . 1 Computing Confidence Intervals under Heteroscedasticity .......475 10.1.2 An Omnibus Test ...................................................479 1 0. 1 .3 R Functions isfitNci, Isfitci, olshc4, hc4test, and hc4wtest .......480 1 0. 1 .4 Comments on Comparing Means via Dummy Coding ...........483 10. 1 .5 Comments on Trying to Salvage the Homoscedasticity Assumption ..........................................................483 10.2 Theil-Sen Estimator ........................................................484 10.2.1 R Functions tsreg, correg, and regplot .............................486 10.3 Least Median of Squares ...................................................487 10.3.1 R Function lmsreg ..................................................487 10.4 Least Trimmed Squares Estimator .........................................488 10.4.1 R Functions ltsreg and Itsgreg ......................................488 10.5 Least Trimmed Absolute Value Estimator ................................488 10.5.1 R Function Itareg ...................................................489 10.6 M-Estimators ...............................................................489 XV Contents 10.7 The Hat Matrix ............................................................ 10.8 Generalized M-Estimators ................................................ 10.8.1 R Function bmreg .................................................. 10.9 The Coakley-Hettmansperger and Yohai Estimators .....................498 10.9.1 MM-Estimator ...................................................... 4 10.9.2 R Functions chreg and MMreg .....................................500 10.10 Skipped Estimators .........................................................500 1 0.10. 1 R Functions mgvreg and opreg .....................................501 10.11 Deepest Regression Line ...................................................502 10.11.1 R Function mdepreg ................................................502 10.12 A Criticism of Methods with a High Breakdown Point ..................503 10.13 Some Additional Estimators ...............................................503 10.13.1 S-Estimators and r-Estimators .....................................503 10. 1 3.2 R Functions snmreg and stsreg .....................................504 10.13.3 E -Туре Skipped Estimators ........................................505 10.13.4 R Functions mbmreg, tstsreg, and gyreg ..........................506 10.13.5 Methods Based on Robust Covariances ...........................507 10.13.6 R Functions bireg, winreg, and COVreg ...........................509 10.13.7 L-Estimators ........................................................510 10.13.8 L , and Quantile Regression ........................................510 10.13.9 R Functions qreg and rqfit ..........................................511 10. 1 3.10 Methods Based on Estimates of the Optimal Weights ............511 10.13.11 Projection Estimators ...............................................512 10.13.12 Methods Based on Ranks ...........................................513 10.14 Comments About Various Estimators .....................................514 10.14.1 Contamination Bias .................................................515 10.15 Outlier Detection Based on a Robust Fit ..................................520 10.15.1 Detecting Regression Outliers .....................................520 1 0.15.2 R Function reglev ...................................................521 10.16 Logistic Regression and the General Linear Model ......................522 1 0.16.1 R Functions glm, logreg, wlogreg, and logreg.plot ...............523 10. 1 6.2 The General Linear Model .........................................524 10.16.3 R Function glmrob ........................................ 525 10.17 Multivariate Regression ................................... 525 10.17.1 The RADA Estimator .................. ///.^........ï.ï............ 526 10. 1 7.2 The Least Distance Estimator ............................ 527 10.17.3 R Functions mlrreg and Mreglde ....................... ! 528 10. 1 7.4 Multivariate Least Trimmed Squares Estimator. 529 10.17.5 R Function MULTtsreg ............................ .530 10.17.6 Other Robust Estimators .................. ! !! 530 10. 1 8 Exercises ......................... ................. XVI Contents Chapter 11 More Regression Methods ............................................533 1 1.1 Inferences About Robust Regression Parameters .........................533 11.2 11.3 11.4 11.5 11.6 1 .1.1 ,1.2 .1.3 .1.4 .1.5 ,1.6 11.1.7 11.1.8 11.1.9 11.1.10 11.1.11 Omnibus Tests for Regression Parameters ........................534 R Function regtest..................................................538 Inferences About Individual Parameters ...........................539 R Functions regci and wlogregci ...................................541 Methods Based on the Quantile Regression Estimator ...........543 R Functions rqtest, qregci, and qrchk ..............................544 Inferences Based on the OP-Estimator ............................545 R Functions opregpb and opregpbMC .............................546 Hypothesis Testing when Using the Multivariate Regression Estimator RADA .......................................547 R Function mlrGtest ................................................548 Robust ANOVA via Dummy Coding ..............................549 Comparing the Parameters of Two Independent Groups .................549 11.2.1 R Function reg2ci ...................................................551 Detecting Heteroscedasticity ...............................................553 11.3.1 A Quantile Regression Approach ..................................553 11.3.2 Koenker s Method ..................................................554 11.3.3 R Functions qhomt and khomreg ..................................555 Curvature and Half-Slope Ratios ..........................................555 11.4.1 R Function hratio ...................................................556 Curvature and Nonparametric Regression ................................558 11.5.1 Smoothers ...........................................................558 11.5.2 Kernel Estimators and Cleveland s LOWESS .....................559 11.5.3 R Functions Iplot and kerreg .......................................561 11.5.4 The Running Interval Smoother ....................................561 11.5.5 R Functions runmean, rungen, runmbo, and runhat...............566 .5.6 Skipped Smoothers .................................................569 .5.7 Smoothers for Estimating Quantiles via Splines ..................569 .5.8 R Function qsmcobs ................................................570 .5.9 Special Methods for Binary Outcomes ............................570 .5.10 R Functions logrsm bkreg, logSM, and rplot.bin ..................572 .5.11 Smoothing with More than One Predictor .........................573 11.5.12 R Functions runm3d, run3hat, rung3d, run3bo, rung3hat, rplot, rplotsm, and runpd ............................................574 11.5.13 LOESS ..............................................................578 11.5.14 Other Approaches ...................................................581 11.5.15 R Function adrun, adrunl, gamplot, and gamplotINT .............583 Checking the Specification of a Regression Model .......................584 Π .6.1 Testing the Hypothesis of a Linear Association ...................585 1 XVII Contents ___________________________________ CQf. 11.6.2 R Function lintest ...................................·······......... 11 .6.3 Testing the Hypothesis of a Generalized Additive Model ........586 11.6.4 R Function adtest ................................................... 587 1 1.6.5 Inferences About the Components of a Generalized Additive Model ...................................................... 588 11.6.6 R Function adcom .................................................. 588 1 1.7 Regression Interactions and Moderator Analysis .........................589 U .7.1 R Functions kercon, riplot, runsm2g, ols.plot.mter, and reg.plot.inter .........................................................591 1 1.7.2 Mediation Analysis .................................................594 1 1 .7.3 R functions ZYmediate, regmed2, and regmediate ...............596 1 1 .8 Comparing Parametric, Additive, and Nonparametric Fits ...............596 11.8.1 R Functions adpchk and pmodchk .................................597 1 1.9 Measuring the Strength of an Association Given a Fit to the Data ......598 It. 9.1 R Function RobRsq .................................................600 1 1.9.2 Comparing Two Independent Groups via Explanatory Power. ... 600 11.9.3 R Functions smcorcom and smstrcom .............................601 11.10 Comparing Predictors .....................................................601 11.10.1 Comparing Pearson Correlations ...................................602 1 1 .10.2 Methods Based on Estimating Prediction Error ...................603 11.10.3 R Functions TWOpov, regpre, andregpreCV .....................605 11.10.4 R Function larsR ....................................................607 11.10.5 Comparing Predictors via Explanatory Power and a Robust Fit ............................................................607 11.10.6 R Functions ts2str and sm2strv7 ...................................608 It. 11 ANCOVA ...................................................................609 11.II.I Methods Based on Specific Design Points ........................610 11.11.2 R Functions ancova, ancpb, runmean2g, Iplot2g, ancboot, ancbbpb, and cobs2g ................................................613 11 . 11 .3 Multiple Covariates .................................................618 1 1. 11 .4 R Functions ancdes, ancovamp, ancmppb, and ancmg ...........619 1 1. II .5 Some Global Tests ..................................................620 11.11.6 R Functions ancsm and Qancsm ...................................624 11.12 Marginal Longitudinal Data Analysis: Comments on Comparing Groups ....................................................................... 624 11 . 1 2. 1 R Functions Iong2g, longreg, longreg.plot, and xyplot ...........626 11.13 Exercises .......................................... ........................................................................631 ■·..............................................................................687 xvin
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spelling	Wilcox, Rand R. Verfasser (DE-588)141426241 aut Introduction to robust estimation and hypothesis testing Rand Wilcox 3. ed. Amsterdam [u.a.] Elsevier, AP 2012 XXI, 690 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier 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 - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027141274&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Wilcox, Rand R. Introduction to robust estimation and 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_auth	Introduction to robust estimation and hypothesis testing
title_exact_search	Introduction to robust estimation and hypothesis testing
title_full	Introduction to robust estimation and hypothesis testing Rand Wilcox
title_fullStr	Introduction to robust estimation and hypothesis testing Rand Wilcox
title_full_unstemmed	Introduction to robust estimation and hypothesis testing Rand Wilcox
title_short	Introduction to robust estimation and hypothesis testing
title_sort	introduction to robust estimation and hypothesis testing
topic	Robuste Schätzung (DE-588)4178265-3 gnd Statistischer Test (DE-588)4077852-6 gnd
topic_facet	Robuste Schätzung Statistischer Test
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027141274&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT wilcoxrandr introductiontorobustestimationandhypothesistesting

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