Introduction to robust estimation and hypothesis testing:
Gespeichert in:
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| Format: | Buch |
| Sprache: | English |
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Amsterdam
AP, Academic Press, an imprint of Elsevier
[2017]
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| Ausgabe: | 4th edition |
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis Seite 741 - 777 |
| Beschreibung: | xxiii, 786 Seiten Illustrationen, Diagramme |
| ISBN: | 9780128047330 |
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| 100 | 1 | |a Wilcox, Rand R. |e Verfasser |0 (DE-588)141426241 |4 aut | |
| 245 | 1 | 0 | |a Introduction to robust estimation and hypothesis testing |c Rand R. Wilcox |
| 250 | |a 4th edition | ||
| 264 | 1 | |a Amsterdam |b AP, Academic Press, an imprint of Elsevier |c [2017] | |
| 264 | 4 | |c © 2017 | |
| 300 | |a xxiii, 786 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverzeichnis Seite 741 - 777 | ||
| 650 | 0 | 7 | |a Robuste Schätzung |0 (DE-588)4178265-3 |2 gnd |9 rswk-swf |
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| adam_text | Contents
Preface......................................................................
Chapter 1: Introduction.................................................... 1
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............................................................ 11
1.7 More Remarks.......................................................... 11
1.8 R Software......................................................... 12
1.9 Some Data Management Issues.......!................................... 15
1.9.1 Eliminating Missing Values.................................... 23
1.10 DataSets.............................................................. 23
Chapter 2: A Foundation for Robust Methods................................... 25
2.1 Basic Tools for Judging Robustness.................................... 25
2.1.1 Qualitative Robustness........................................ 26
2.1.2 Infinitesimal Robustness..................................... 29
2.1.3 Quantitative Robustness....................................... 30
2.2 Some Measures of Location and Their Influence Function................ 31
2.2.1 Quantiles..................................................... 31
2.2.2 The Winsorized Mean........................................... 32
2.2.3 The Trimmed Mean.............................................. 34
2.2.4 M-Measures of Location........................................ 34
2.2.5 R-Measures of Location........................................ 37
2.3 Measures of Scale..................................................... 38
2.4 Scale Equivariant M-Measures of Location.............................. 40
2.5 Winsorized Expected Values............................................ 41
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Contents
Chapter 3: Estimating Measures of Location and Scale........................... 45
3.1 A Bootstrap Estimate of a Standard Error............................. 45
3.1.1 R Function bootse.............................................. 47
3.2 Density Estimators...................................................... 48
3.2.1 Silverman’s Rule of Thumb...................................... 49
3.2.2 Rosenblatt’s Shifted Histogram................................. 49
3.2.3 The Expected Frequency Curve................................... 50
3.2.4 An Adaptive Kernel Estimator................................... 51
3.2.5 R Functions skerd, kerSORT, kerden, kdplot, rdplot, akerd and splot 52
3.3 The Sample Trimmed Mean................................................ 57
3.3.1 R Functions mean, tmean and Hoc.............................. 59
3.3.2 Estimating the Standard Error of the Trimmed Mean.............. 60
3.3.3 Estimating the Standard Error of the Sample Winsorized Mean. 64
3.3.4 R Functions winmean, winvar, trimse and winse.................. 65
3.3.5 Estimating the Standard Error of the Sample Median............. 65
3.3.6 R Function msmedse............................................. 66
3.4 The Finite Sample Breakdown Point....................................... 66
3.5 Estimating Quantiles.................................................... 67
3.5.1 Estimating the Standard Error of the Sample Quantile........... 68
3.5.2 R Function qse................................................. 69
3.5.3 The Maritz-Jarrett Estimate of the Standard Error of xq........ 70
3.5.4 R Function mjse................................................ 71
3.5.5 The Harrell-Davis Estimator.................................... 71
3.5.6 R Functions qest and hd........................................ 72
3.5.7 A Bootstrap Estimate of the Standard Error of 9q............... 73
3.5.8 R Function hdseb............................................... 73
3.6 An M-Estimator of Location............................................. 73
3.6.1 R Function mad............................................... 78
3.6.2 Computing an M-Estimator of Location........................... 79
3.6.3 R Functions mest............................................... 80
3.6.4 Estimating the Standard Error of the M-Estimator............... 81
3.6.5 R Function mestse.............................................. 83
3.6.6 A Bootstrap Estimate of the Standard Error of jlm.............. 84
3.6.7 R Function mestseb............................................. 84
3.7 One-Step M-Estimator.................................................... 85
3.7.1 R Function onestep............................................. 86
3.8 W-Estimators............................................................ 86
3.8.1 Tau Measure of Location........................................ 87
3.8.2 R Function tauloc.............................................. 88
3.8.3 Zuo’s Weighted Estimator....................................... 88
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Contents
3.9 The Hodges-Lehmann Estimator............................................. 89
3.10 Skipped Estimators....................................................... 89
3.10.1 R Functions mom and bmean....................................... 90
3.11 Some Comparisons of the Location Estimators.............................. 90
3.12 More Measures of Scale................................................... 93
3.12.1 The Biweight Midvariance........................................ 94
3.12.2 R Function bivar................................................ 96
3.12.3 The Percentage Bend Midvariance and Tau Measure of Variation... 96
3.12.4 R Functions pbvar, tauvar....................................... 98
3.12.5 The Interquartile Range......................................... 99
3.12.6 R Functions idealf and idrange.................................. 99
3.13 Some Outlier Detection Methods.......................................... 100
3.13.1 Rules Based on Means and Variances............................. 100
3.13.2 A Method Based on the Interquartile Range...................... 101
3.13.3 Carling’s Modification......................................... 101
3.13.4 A MAD-Median Rule.............................................. 101
3.13.5 R Functions outbox, out and boxplot............................ 102
3.13.6 R Functions adjboxout and adjbox............................... 104
3.14 Exercises............................................................. 105
Chapter 4: Confidence Intervals in the One-Sample Case.......................... 107
4.1 Problems when Working with Means........................................ 107
4.2 The g-and-h Distribution................................................ Ill
4.2.1 R Functions ghdist, rmul, mgh and ghtrim....................... 114
4.3 Inferences About the Trimmed and Winsorized Means....................... 115
4.3.1 R Functions trimci, winci and D.akp.effect..................... 120
4.4 Basic Bootstrap Methods................................................. 120
4.4.1 The Percentile B ootstrap Method............................... 121
4.4.2 R Functions onesampb and hdpb.................................. 122
4.4.3 Bootstrap-t Method............................................. 123
4.4.4 Bootstrap Methods when Using a Trimmed Mean.................... 125
4.4.5 Singh’s Modification........................................... 129
4.4.6 R Functions trimpb and trimcibt................................ 130
4.5 Inferences About M-Estimators........................................... 130
4.5.1 R Functions mestci and momci................................... 132
4.6 Confidence Intervals for Quantiles...................................... 133
4.6.1 Beware of Tied Values when Making Inferences About Quantiles .. 136
4.6.2 A Modification of the Distribution-Free Method for the Median .... 137
4.6.3 R Functions qmjci, hdci, sint, sintv2, qci, qcipb and qint..... 138
4.7 Empirical Likelihood.................................................... 140
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Contents
4.7.1 Bartlett Corrected Empirical Likelihood...................... 140
4.8 Concluding Remarks.................................................... 142
4.9 Exercises............................................................. 143
Chapter 5: Comparing Two Croups................................................ 145
5.1 The Shift Function.................................................... 146
5.1.1 The Kolmogorov-Smimov Test................................... 149
5.1.2 R Functions ks, kssig, kswsig, and kstiesig.................. 152
5.1.3 The B and W Band for the Shift Function...................... 153
5.1.4 R Functions sband and wband.................................. 155
5.1.5 Confidence Band for Specified Quantiles................... 158
5.1.6 R Functions shifthd, qcomhd, qcomhdMC and q2gci.............. 160
5.1.7 R Functions g2plot and g5plot................................ 161
5.2 Student’s t Test................................................... 162
5.3 Comparing Medians and Other Trimmed Means............................. 166
5.3.1 R Functions yuen and msmed................................... 169
5.3.2 A Bootstrap-t Method for Comparing Trimmed Means............. 170
5.3.3 R Functions yuenbt and yhbt.................................. 173
5.3.4 Measuring Effect Size........................................ 176
5.3.5 R Functions akp.effect, yuenv2, ees.ci, med.effect and qhat. 180
5.4 Inferences Based on a Percentile Bootstrap Method..................... 182
5.4.1 Comparing M-Estimators....................................... 183
5.4.2 Comparing Trimmed Means and Medians.......................... 184
5.4.3 R Functions trimpb2, pb2gen, m2ci, medpb2 and M2gbt.......... 185
5.5 Comparing Measures of Scale........................................... 187
5.5.1 Comparing Variances........................................ 187
5.5.2 R Function comvar2........................................... 188
5.5.3 Comparing Biweight Midvariances............................ 188
5.5.4 R Function b2ci.............................................. 189
5.6 Permutation Tests .................................................... 189
5.6.1 R Function permg............................................. 190
5.7 Rank-Based Methods and a Probabilistic Measure of Effect Size......... 190
5.7.1 The Cliff and Brunner-Munzel Methods......................... 192
5.7.2 R Functions cid, cidv2, bmp, wmwloc, wmwpb and loc2plot..... 195
5.8 Comparing Two Independent Binomial and Multinomial Distributions .... 198
•5.8.1 Storer-Kim Method............................................ 200
5.8.2 Beal’s Method................................................ 200
5.8.3 KMS Method................................................... 201
5.8.4 R Functions twobinom, twobici, bi2KMS, bi2KMSv2 and bi2CR .. 201
5.8.5 Comparing Discrete (Multinomial) Distributions............... 202
•••
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5.8.6 R Functions binband, splotg2, cumrelf......................... 203
5.9 Comparing Dependent Groups........................................... 205
5.9.1 A Shift Function for Dependent Groups......................... 206
5.9.2 R Function lband.............................................. 207
5.9.3 Comparing Specified Quantiles................................. 207
5.9.4 R Functions shiftdhd, Dqcomhd, qdec2, Dqdif and difQpci...... 210
5.9.5 Comparing Trimmed Means....................................... 212
5.9.6 R Functions yuend, yuendv2 and D.akp.effect................... 215
5.9.7 A Bootstrap-t Method for Marginal Trimmed Means............... 217
5.9.8 R Function ydbt............................................... 217
5.9.9 Inferences About the Distribution of Difference Scores........ 217
5.9.10 R Functions loc2dif and 12drmci............................... 219
5.9.11 Percentile Bootstrap: Comparing Medians, M-Estimators and Other
Measures of Location and Scale............................... 220
5.9.12 R Function bootdpci........................................... 221
5.9.13 Handling Missing Values....................................... 222
5.9.14 R Functions rm2miss and rmmismcp.............................. 226
5.9.15 Comparing Variances........................................... 227
5.9.16 R Function comdvar............................................ 228
5.9.17 The Sign Test and Inferences About the Binomial Distribution. 228
5.9.18 R Functions binomci, acbinomci and binomLCO................... 231
5.10 Exercises............................................................. 232
Chapter 6: Some Multivariate Methods............................................ 235
6.1 Generalized Variance.................................................. 235
6.2 Depth.................................................................. 236
6.2.1 Mahalanobis Depth............................................. 236
6.2.2 Halfspace Depth............................................... 236
6.2.3 Computing Halfspace Depth.................................... 239
6.2.4 R Functions depth2, depth, fdepth, fdepthv2, unidepth......... 241
6.2.5 Projection Depth............................................. 242
6.2.6 R Functions pdis, pdisMC, and pdepth.......................... 243
6.2.7 Other Measures of Depth....................................... 244
6.2.8 R Functions zdist, zoudepth and prodepth...................... 245
6.3 Some Affine Equivariant Estimators..................................... 245
6.3.1 Minimum Volume Ellipsoid Estimator............................ 247
6.3.2 The Minimum Covariance Determinant Estimator.................. 247
6.3.3 S-Estimators and Constrained M-Estimators..................... 248
6.3.4 R Function tbs.............................................. 249
6.3.5 Donoho-Gasko Generalization of a Trimmed Mean ................ 249
Contents
6.3.6 R Functions dmean and dcov..................................... 250
6.3.7 The Stahel-Donoho W-Estimator.................................. 252
6.3.8 R Function sdwe................................................ 253
6.3.9 Median Ball Algorithm.......................................... 253
6.3.10 R Function rmba................................................ 253
6.3.11 OGK Estimator.................................................. 254
6.3.12 R Function ogk................................................. 255
6.3.13 An M-Estimator................................................ 255
6.3.14 R Functions MARest and dmedian................................. 256
6.4 Multivariate Outlier Detection Methods................................ 257
6.4.1 A Relplot.................................................... 258
6.4.2 R Function relplot............................................ 260
6.4.3 The MVE Method................................................. 260
6.4.4 The MCD Method................................................. 261
6.4.5 R Functions covmve and covmcd.................................. 261
6.4.6 R Function out................................................. 262
6.4.7 The MGV Method................................................. 263
6.4.8 R Function outmgv.............................................. 265
6.4.9 A Projection Method............................................ 266
6.4.10 R Functions outpro and out3d................................... 268
6.4.11 Outlier Identification in High Dimensions...................... 269
6.4.12 R Functions outproad and outmgvad.............................. 270
6.4.13 Methods Designed for Functional Data........................... 270
6.4.14 R Functions FBplot, Flplot, medcurve, func.out, spag.plot, funloc
and funlocpb................................................... 272
6.4.15 Comments on Choosing a Method.................................. 275
6.5 A Skipped Estimator of Location and Scatter........................... 277
6.5.1 R Functions smean, wmcd, wmve, mgvmean, LI medcen, spat,
mgvcov, skip, skipcov.......................................... 278
6.6 Robust Generalized Variance........................................... 280
6.6.1 R Function gvarg............................................... 280
6.7 Multivariate Location: Inference in the One-Sample Case............... 281
6.7.1 Inferences Based on the OP Measure of Location................. 281
6.7.2 Extension of Hotelling’s T2 to Trimmed Means................... 282
6.7.3 RFunctionssmeancrv2andhotell.tr................................ 283
■6.7.4 Inferences Based on the MGV Estimator.......................... 284
6.7.5 R Function smgvcr.............................................. 285
6.8 Comparing OP Measures of Location..................................... 285
6.8.1 R Functions smean2, matsplit and mat2grp....................... 286
6.8.2 Comparing Robust Generalized Variances......................... 287
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Contents
6.8.3 R Function gvar2g........................................... 287
6.9 Multivariate Density Estimators..................................... 288
6.10 A Two-Sample, Projection-Type Extension of the
Wilcoxon-Mann-Whitney Test........................................... 289
6.10.1 R Functions mulwmw and mulwmwv2............................. 291
6.11 A Relative Depth Analog of the Wilcoxon-Mann-Whitney Test........... 292
6.11.1 R Function mwmw............................................. 294
6.12 Comparisons Based on Depth.......................................... 296
6.12.1 R Functions lsqs3 and depthg2............................... 298
6.13 Comparing Dependent Groups Based on All Pairwise Differences......... 300
6.13.1 R Function dfried........................................... 302
6.14 Robust Principal Components Analysis............................... 302
6.14.1 R Functions prcomp and regpca............................... 304
6.14.2 Maronna’s Method............................................ 305
6.14.3 The SPCA Method............................................. 305
6.14.4 Method HRVB................................................. 306
6.14.5 Method OP.................................................. 306
6.14.6 Method PPCA................................................. 307
6.14.7 R Functions outpca, robpca, robpcaS, SPCA, Ppca, Ppca.summary. 308
6.14.8 Comments on Choosing the Number of Components............... 309
6.15 Cluster Analysis..................................................... 313
6.15.1 R Functions Kmeans, kmeans.grp, TKmeans, TKmeans.grp. 314
6.16 Multivariate Discriminate Analysis.................................. 315
6.16.1 R Function KNNdist.......................................... 316
6.17 Exercises......................................................... 317
Chapter 7: One-Way and Higher Designs for Independent Croups................... 319
7.1 Trimmed Means and a One-Way Design.................................. 320
7.1.1 A Welch-Type Procedure and a Robust Measure of Effect Size... 321
7.1.2 R Functions tlway, tlwayv2, esmcp, fac21ist, tlwayF... 323
7.1.3 A Generalization of Box’s Method............................ 327
7.1.4 R Function box 1 way........................................ 328
7.1.5 Comparing Medians and Other Quantiles....................... 328
7.1.6 R Functions medl way and Qanova............................. 330
7.1.7 A Bootstrap-t Method........................................ 330
7.1.8 R Functions tlwaybt and btrim............................... 331
7.2 Two-Way Designs and Trimmed Means................................... 333
7.2.1 R Function t2way............................................ 337
7.2.2 Comparing Medians........................................... 339
7.2.3 R Functions med2way and Q2anova............................. 341
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7.3 Three-Way Designs and Trimmed Means Including Medians................ 341
7.3.1 R Functions t3way, fac21ist and Q3anova....................... 343
7.4 Multiple Comparisons Based on Medians and Other Trimmed Means........ 346
7.4.1 Basic Methods Based on Trimmed Means.......................... 347
7.4.2 R Functions lincon, conCON and stepmcp........................ 349
7.4.3 Multiple Comparisons for Two-Way and Three-Way Designs...... 354
7.4.4 R Functions bbmcp, mcp2med, bbbmcp, mcp3med, con2way and
con3way..................................................... 355
7.4.5 A Bootstrap-t Procedure....................................... 357
7.4.6 R Functions linconb, bbtrim and bbbtrim....................... 359
7.4.7 Controlling the Familywise Error Rate: Improvements on the
Bonferroni Method........................................... 361
7.4.8 R Functions p.adjust and mcpKadjp............................. 364
7.4.9 Percentile Bootstrap Methods for Comparing Medians, Other
Trimmed Means and Quantiles................................... 365
7.4.10 R Functions linconpb, bbmcppb, bbbmcppb, medpb, Qmcp,
med2mcp, med3mcp and q2by2.................................... 365
7.4.11 Judging Sample Sizes.......................................... 368
7.4.12 R Function hochberg........................................... 369
7.4.13 Explanatory Measure of Effect Size............................ 370
7.4.14 R Functions ESmainMCP and eslmcp.............................. 370
7.4.15 Comparing Curves (Functional Data)............................ 371
7.4.16 R Functions funyuenpb and Flplot2g............................ 372
7.5 A Random Effects Model for Trimmed Means............................. 372
7.5.1 A Winsorized Intraclass Correlation........................... 373
7.5.2 R Function rananova........................................... 376
7.6 Global Tests Based on M-Measures of Location......................... 376
7.6.1 R Functions b 1 way and pbadepth.............................. 380
7.6.2 M-Estimators and Multiple Comparisons......................... 381
7.6.3 R Functions linconm and pbmcp................................. 384
7.6.4 M-Estimators and the Random Effects Model..................... 385
7.6.5 Other Methods for One-Way Designs............................. 385
7.7 M-Measures of Location and a Two-Way Design.......................... 385
7.7.1 R Functions pbad2way and mcp2a................................ 388
7.8 Ranked-Based Methods for a One-Way Design............................ 389
7.8.1 The Rust-Fligner Method....................................... 389
7.8.2 R Function rfanova............................................ 391
7.8.3 A Heteroscedastic Rank-Based Method That Allows Tied Values... 391
7.8.4 R Function bdm................................................ 391
7.8.5 Inferences About a Probabilistic Measure of Effect Size....... 393
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7.8.6 R Functions cidmulv2, wmwaov and cidM........................ 395
7.9 A Rank-Based Method for a Two-Way Design............................. 396
7.9.1 R Function bdm2way........................................... 397
7.9.2 The Patel-Hoel Approach to Interactions...................... 398
7.9.3 R Function rimul............................................. 400
7.10 MANOVA Based on Trimmed Means........................................ 400
7.10.1 R Functions MULtr.anova, MULAOVp, bw21ist and YYmanova ... 403
7.10.2 Linear Contrasts............................................. 405
7.10.3 R Functions linconMpb, linconSpb, YYmcp, fac2Mlist and
fac2BBMlist................................................ 407
7.11 Nested Designs....................................................... 409
7.11.1 R Functions anova.nestA, mcp.nestA and anova.nestAP.......... 412
7.12 Exercises............................................................ 413
Chapter 8: Comparing Multiple Dependent Croups................................ 417
8.1 Comparing Trimmed Means............................................ 417
8.1.1 Omnibus Test Based on the Trimmed Means of the Marginal
Distributions................................................ 418
8.1.2 R Function rmanova........................................... 418
8.1.3 Pairwise Comparisons and Linear Contrasts Based on Trimmed
Means........................................................ 420
8.1.4 Linear Contrasts Based on the Marginal Random Variables..... 423
8.1.5 R Functions rmmcp, rmmismcp and trimcimul.................... 424
8.1.6 Judging the Sample Size...................................... 424
8.1.7 RFunctionssteinl.trandstein2.tr.............................. 426
8.2 Bootstrap Methods Based on Marginal Distributions.................... 426
8.2.1 Comparing Trimmed Means...................................... 427
8.2.2 R Function rmanovab.......................................... 427
8.2.3 Multiple Comparisons Based on Trimmed Means.................. 428
8.2.4 R Functions pairdepb and bptd................................ 429
8.2.5 Percentile Bootstrap Methods............................... 431
8.2.6 R Functions bdlway, ddep and ddepGMC_C....................... 434
8.2.7 Multiple Comparisons Using M-Estimators or Skipped Estimators . 436
8.2.8 R Functions lindm and mcpOV.................................. 437
8.3 Bootstrap Methods Based on Difference Scores......................... 439
8.3.1 R Function rmdzero........................................... 440
8.3.2 Multiple Comparisons......................................... 442
8.3.3 R Functions rmmcppb, wmcppb, dmedpb, lindepbt and qdmcpdif.. 443
8.4 Comments on Which Method to Use...................................... 445
8.5 Some Rank-Based Methods.............................................. 447
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8.5.1 R Functions apanova and bprra............................... 449
8.6 Between-by-Within and Within-by-Within Designs....................... 449
8.6.1 Analyzing a Between-by-Within Design Based on Trimmed Means 449
8.6.2 R Functions bwtrim and tsplit............................... 451
8.6.3 Data Management: R Function bw21ist......................... 454
8.6.4 Bootstrap-t Method for a Between-by-Within Design........... 455
8.6.5 R Functions bwtrimbt and tsplitbt........................... 456
8.6.6 Percentile Bootstrap Methods for a Between-by-Within Design. 456
8.6.7 R Functions sppba, sppbb and sppbi.......................... 458
8.6.8 Multiple Comparisons........................................ 459
8.6.9 R Functions bwmcp, bwamcp, bwbmcp, bwimcp, bwimcpES,
spmcpa, spmcpb and spmcpi................................... 463
8.6.10 Within-by-Within Designs.................................... 465
8.6.11 R Functions wwtrim, wwtrimbt, wwmcp, wwmcppb and wwmcpbt 466
8.6.12 A Rank-Based Approach....................................... 467
8.6.13 R Function bwrank........................................... 470
8.6.14 Rank-Based Multiple Comparisons............................. 472
8.6.15 R Function bwrmcp........................................... 472
8.6.16 Multiple Comparisons when Using a Patel-Hoel Approach to
Interactions................................................ 473
8.6.17 R Function sisplit.......................................... 474
8.7 Some Rank-Based Multivariate Methods................................. 474
8.7.1 The Munzel-Brunner Method................................... 475
8.7.2 R Function mulrank.......................................... 476
8.7.3 The Choi-Marden Multivariate Rank Test...................... 477
8.7.4 R Function cmanova.......................................... 479
8.8 Three-Way Designs.................................................... 479
8.8.1 Global Tests Based on Trimmed Means......................... 480
8.8.2 R Functions bbwtrim, bwwtrim, wwwtrim, bbwtrimbt, bwwtrimbt
andwwwtrimbt................................................ 481
8.8.3 Data Management: R Functions bw21ist and bbw21ist........... 481
8.8.4 Multiple Comparisons....................................... 482
8.8.5 R Function wwwmcp........................................... 483
8.8.6 R Functions bbwmcp, bwwmcp, bbwmcppb, bwwmcppb and
wwwmcppb.................................................... 483
8.9 Exercises............................................................ 484
Chapter 9: Correlation and Tests of Independence.............................. 485
9.1 Problems with Pearson’s Correlation.................................. 485
9.1.1 Features of Data That Affect r and T........................ 488
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9.1.2 Heteroscedasticity and the Classic Test that p = 0.............. 489
9.2 Two Types of Robust Correlations......................................... 490
9.3 Some Type M Measures of Correlation...................................... 490
9.3.1 The Percentage Bend Correlation................................. 490
9.3.2 A Test of Independence Based on ppb............................. 491
9.3.3 R Function pbcor................................................ 493
9.3.4 A Test of Zero Correlation Among p Random Variables............. 493
9.3.5 R Function pball................................................ 495
9.3.6 The Winsorized Correlation...................................... 496
9.3.7 R Functions wincor and winall .................................. 497
9.3.8 The Biweight Midcovariance and Correlation...................... 498
9.3.9 R Functions bicov and bicovm.................................... 499
9.3.10 Kendall’s tau.................................................. 500
9.3.11 Spearman’s rho.................................................. 501
9.3.12 R Functions tau, spear, cor and taureg.......................... 502
9.3.13 Heteroscedastic Tests of Zero Correlation....................... 503
9.3.14 R Functions corb, pcorb and pcorhc4............................. 504
9.4 Some Type O Correlations................................................. 504
9.4.1 MVE and MCD Correlations........................................ 505
9.4.2 Skipped Measures of Correlation................................. 505
9.4.3 The OP Correlation.............................................. 505
9.4.4 Inferences Based on Multiple Skipped Correlations............... 506
9.4.5 R Functions scor, mscor and scorci.............................. 508
9.5 A Test of Independence Sensitive to Curvature............................ 509
9.5.1 R Functions indt, indtall and medind............................ 512
9.6 Comparing Correlations: Independent Case................................. 513
9.6.1 Comparing Pearson Correlations.................................. 513
9.6.2 Comparing Robust Correlations................................... 514
9.6.3 R Functions twopcor, twohc4cor and twocor ...................... 514
9.7 Exercises................................................................ 515
Chapter 10: Robust Regression...................................i................ 5/7
10.1 Problems with Ordinary Least Squares..................................... 518
10.1.1 Computing Confidence Intervals Under Heteroscedasticity......... 521
10.1.2 An Omnibus Test................................................. 526
10.1.3 R Functions lsfitci, olshc4, hc4test and hc4wtest............... 527
10.1.4 Comments on Comparing Means via Dummy Coding.................... 529
10.1.5 Salvaging the Homoscedasticity Assumption....................... 529
10.2 Theil-Sen Estimator...................................................... 530
10.2.1 R Functions tsreg, tshdreg, correg, regplot and regp2plot....... 533
xv
Contents
10.3 Least Median of Squares............................................... 535
10.3.1 R Function lmsreg............................................. 535
10.4 Least Trimmed Squares Estimator........................................ 535
10.4.1 R Functions Itsreg and Itsgreg................................ 536
10.5 Least Trimmed Absolute Value Estimator................................. 536
10.5.1 R Function ltareg............................................. 537
10.6 M-Estimators......................................................... 537
10.7 The Hat Matrix......................................................... 538
10.8 Generalized M-Estimators............................................... 541
10.8.1 R Function bmreg.............................................. 545
10.9 The Coakley-Hettmansperger and Yohai Estimators........................ 545
10.9.1 MM-Estimator.................................................. 547
10.9.2 R Functions chreg and MMreg................................... 548
10.10 Skipped Estimators..................................................... 549
10.10.1 R Functions mgvreg and opreg.................................. 549
10.11 Deepest Regression Line................................................ 550
10.11.1 R Functions rdepth and mdepreg................................ 551
10.12 A Criticism of Methods with a High Breakdown Point..................... 551
10.13 Some Additional Estimators............................................. 551
10.13.1 S-Estimators and r-Estimators................................. 552
10.13.2 R Functions snmreg and stsreg................................. 553
10.13.3 E-Type Skipped Estimators..................................... 553
10.13.4 R Functions mbmreg, tstsreg, tssnmreg and gyreg............... 555
10.13.5 Methods Based on Robust Covariances........................... 556
10.13.6 R Functions bireg, winreg and COVreg.......................... 558
10.13.7 L-Estimators.................................................. 559
10.13.8 L and Quantile Regression.................................... 559
10.13.9 R Functions qreg, rqfit, qplotreg............................. 560
10.13.10 Methods Based on Estimates of the Optimal Weights............. 561
10.13.11 Projection Estimators......................................... 562
10.13.12 Methods Based on Ranks........................................ 562
10.13.13 RFunctionsRfitandRfit.est.................................... 564
10.13.14 Empirical Likelihood Type and Distance-Constrained Maximum
Likelihood Estimators......................................... 565
10.14 Comments About Various Estimators...................................... 565
10.14.1 Contamination Bias............................................ 567
10.15 Outlier Detection Based on a Robust Fit.............................. 571
10.15.1 Detecting Regression Outliers................................. 571
10.15.2 R Functions reglev and rmblo.................................. 571
10.16 Logistic Regression and the General Linear Model..................... 573
XVI
Contents
10.16.1 R Functions glm, logreg, wlogreg, logreg.plot.................. 575
10.16.2 The General Linear Model....................................... 576
10.16.3 R Function glmrob............................................... 576
10.17 Multivariate Regression............................................... 577
10.17.1 The RADA Estimator.............................................. 578
10.17.2 The Least Distance Estimator.................................... 579
10.17.3 R Functions MULMreg, mlrreg and Mreglde......................... 579
10.17.4 Multivariate Least Trimmed Squares Estimator.................. 581
10.17.5 R Function MULtsreg............................................. 581
10.17.6 Other Robust Estimators....................................... 582
10.18 Exercises............................................................. 582
Chapter 11: More Regression Methods..............................................
11.1 Inferences About Robust Regression Parameters............................ 585
11.1.1 Omnibus Tests for Regression Parameters......................... 586
11.1.2 R Function regtest.............................................. 590
11.1.3 Inferences About Individual Parameters.......................... 591
11.1.4 R Functions regci, regciMC and wlogregci........................ 593
11.1.5 Methods Based on the Quantile Regression Estimator.............. 595
11.1.6 R Functions rqtest, qregci and qrchk............................ 597
11.1.7 Inferences Based on the OP Estimator............................ 598
11.1.8 R Functions opregpb and opregpbMC............................... 600
11.1.9 Hypothesis Testing when Using a Multivariate Regression
Estimator RADA.................................................. 600
11.1.10 R Function mlrGtest............................................ 601
11.1.11 Robust ANOVA via Dummy Coding................................... 601
11.1.12 Confidence Bands for the Typical Value of y Given x ............ 602
11.1.13 R Functions regYhat, regYci, andregYband........................ 604
11.1.14 R Function regse.............................................. 606
11.2 Comparing the Regression Parameters of J 2 Groups....................... 606
11.2.1 Methods for Comparing Independent Groups....;................... 606
11.2.2 R Functions reg2ci, reglway, reglwaylSO, ancGpar, olslway,
olslwaylSO, olsJmcp, olsJ2, reglmcp and olsWmcp................. 612
11.2.3 Methods for Comparing Two Dependent Groups...................... 616
11.2.4 R Functions DregG, difreg, DregGOLS............................. 618
11.3 Detecting Heteroscedasticity............................................. 618
11.3.1 A Quantile Regression Approach.................................. 619
11.3.2 Koenker-Bassett Method.......................................... 620
11.3.3 R Functions qhomt and khomreg................................... 620
xvii
Contents
11.4 Curvature and Half-Slope Ratios........................................ 621
11.4.1 R Function hratio............................................. 622
11.5 Curvature and Nonparametric Regression................................. 623
11.5.1 Smoothers...................................................... 624
11.5.2 Kernel Estimators and Cleveland’s LOWESS....................... 624
11.5.3 R Functions lplot, lplot.pred and kerreg....................... 626
11.5.4 The Running-Interval Smoother.................................. 628
11.5.5 R Functions rplot and runYhat.................................. 633
11.5.6 Smoothers for Estimating Quantiles............................. 635
11.5.7 R Function qhdsm .............................................. 636
11.5.8 Special Methods for Binary Outcomes............................ 637
11.5.9 R Functions logSM, logSMpred, bkreg and rplot.bin.............. 638
11.5.10 Smoothing with More than One Predictor......................... 639
11.5.11 R Functions rplot, runYhat, rplotsm and runpd.................. 640
11.5.12 LOESS.......................................................... 644
11.5.13 Other Approaches............................................... 647
11.5.14 R Functions adrun, adrunl, gamplot, gamplotINT................. 648
11.6 Checking the Specification of a Regression Model....................... 649
11.6.1 Testing the Hypothesis of a Linear Association................. 650
11.6.2 R Function lintest............................................. 651
11.6.3 Testing the Hypothesis of a Generalized Additive Model......... 652
11.6.4 R Function adtest.............................................. 653
11.6.5 Inferences About the Components of a Generalized Additive Model 653
11.6.6 R Function adcom............................................... 654
11.6.7 Detecting Heteroscedasticity Based on Residuals................ 654
11.6.8 R Function rhom.............................................. 655
11.7 Regression Interactions and Moderator Analysis......................... 655
11.7.1 R Functions kercon, riplot, runsm2g, ols.plot.inter, olshc4.inter,
reg.plotinter and regci.inter.................................. 657
11.7.2 Mediation Analysis............................................. 661
11.7.3 R Functions ZYmediate, regmed2 and regmediate.................. 663
11.8 Comparing Parametric, Additive and Nonparametric Fits.................. 664
11.8.1 R Functions adpchk and pmodchk................................. 664
11.9 Measuring the Strength of an Association Given a Fit to the Data....... 666
11.9.1 R Functions RobRsq, qcorpl and qcor............................ 669
* 11.9.2 Comparing Two Independent Groups via the LOWESS Version of
Explanatory Power.............................................. 670
11.9.3 R Functions smcorcom and smstrcom.. *.......................... 671
11.10 Comparing Predictors................................................... 671
11.10.1 Comparing Correlations....................................... 672
xvin
Contents
11.10.2 R Functions TWOpov, TWOpNOV, corCOMmcp, twoDcorR, and
twoDNOV....................................................... 675
11.10.3 Methods Based on Prediction Error............................. 676
11.10.4 R Functions regpre and regpreCV............................... 678
11.10.5 R Function larsR.............................................. 680
11.10.6 Inferences About Which Predictors Are Best.................... 681
11.10.7 R Functions regIVcom, ts2str and sm2strv7..................... 686
11.11 Marginal Longitudinal Data Analysis: Comments on Comparing Groups.. 687
11.11.1 R Functions long2g, longreg, longreg.plot and xyplot.......... 689
11.12 Exercises.............................................................. 690
Chapter 12: ANCOVA............................................................. 693
12.1 Methods Based on Specific Design Points and a Linear Model............ 695
12.1.1 Method SI .................................................... 696
12.1.2 Method S2..................................................... 696
12.1.3 Dealing with Two Covariates................................... 698
12.1.4 R Functions ancJN, ancJNmp, ancJNmpcp, anclin, reg2plot and
reg2g.p2plot.................................................. 699
12.2 Methods when There Is Curvature and a Single Covariate............... 702
12.2.1 Method Y...................................................... 703
12.2.2 Method BB: Bootstrap Bagging.................................. 705
12.2.3 Method UB ................................................... 706
12.2.4 Method TAP.................................................... 707
12.2.5 Method G...................................................... 708
12.2.6 R Functions ancova, ancovaWMW, ancpb, rplot2g, runmean2g,
lplot2g, ancdifplot, ancboot, ancbbpb, qhdsm2g, ancovaUB,
ancovaUB.pv, ancdet, ancmgl and ancGLOB....................... 710
12.3 Dealing with Two Covariates when There Is Curvature................... 719
12.3.1 Method MCI.................................................. 719
12.3.2 Method MC2.................................................... 720
12.3.3 Method MC3.................................................. 722
12.3.4 R Functions ancovamp, ancovampG, ancmppb, ancmg,
ancov2COV, ancdes and ancdet2C................................ 723
12.4 Some Global Tests.................................................... 731
12.4.1 Method TG..................................................... 731
12.4.2 R Functions ancsm and Qancsm.................................. 734
12.5 Methods for Dependent Groups......................................... 735
12.5.1 Methods Based on a Linear Model............................... 735
12.5.2 R Functions Dancts and Dancols................................ 736
12.5.3 Dealing with Curvature: Methods DY, DUB and DTAP.............. 736
xix
Contents
12.5.4 R Functions Dancova, Dancovapb, DancovaUB and Dancdet..... 737
12.6 Exercises........................................................... 740
References.................................................................... 741
Index......................................................................... 779
xx
|
| any_adam_object | 1 |
| author | Wilcox, Rand R. |
| author_GND | (DE-588)141426241 |
| author_facet | Wilcox, Rand R. |
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| bvnumber | BV043907032 |
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| discipline | Psychologie Mathematik Wirtschaftswissenschaften |
| edition | 4th edition |
| format | Book |
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| indexdate | 2024-07-10T07:38:11Z |
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| isbn | 9780128047330 |
| language | English |
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| spelling | Wilcox, Rand R. Verfasser (DE-588)141426241 aut Introduction to robust estimation and hypothesis testing Rand R. Wilcox 4th edition Amsterdam AP, Academic Press, an imprint of Elsevier [2017] © 2017 xxiii, 786 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Literaturverzeichnis Seite 741 - 777 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 Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029316152&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 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 | 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=029316152&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT wilcoxrandr introductiontorobustestimationandhypothesistesting |