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E-raamat: Introduction to Robust Estimation and Hypothesis Testing

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  • ISBN-13: 9780128047811
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Introduction to Robust Estimation and Hypothesis TestingSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 02-Sep-2016
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780128047811
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Introduction to Robust Estimating and Hypothesis Testing 4th editon is a ‘how-to’ on the application of robust methods using available software. Modern robust methods provide improved techniques for dealing with outliers, skewed distribution curvature and heteroscedasticity that can provide substantial gains in power as well as a deeper, more accurate and more nuanced understanding of data. Since the last edition, there have been numerous advances and improvements. They include new techniques for comparing groups and measuring effect size as well as new methods for comparing quantiles. Many new regression methods have been added that include both parametric and nonparametric techniques. The methods related to ANCOVA have been expanded considerably. New perspectives related to discrete distributions with a relatively small sample space are described as well as new results relevant to the shift function. The practical importance of these methods is illustrated using data from real world studies. The R package written for this book now contains over 1200 functions.

New to this edition

  • 35% revised content
  • Covers many new and improved R functions
  • New techniques that deal with a wide range of situations
  • Extensive revisions to cover the latest developments in robust regression
  • Covers latest improvements in ANOVA
  • Includes newest rank-based methods
  • Describes and illustrated easy to use software

Muu info

This work describes and illustrates modern robust methods for dealing with outliers, skewed distributions, heteroscedasticity and curvature for anyone dealing with methods for studying associations, comparing groups, or analyzing multivariate data
Preface xxi
Chapter 1 Introduction
1(24)
1.1 Problems with Assuming Normality
2(4)
1.2 Transformations
6(1)
1.3 The Influence Curve
7(1)
1.4 The Central Limit Theorem
8(1)
1.5 Is the ANOVA F Robust?
9(2)
1.6 Regression
11(1)
1.7 More Remarks
11(1)
1.8 R Software
12(3)
1.9 Some Data Management Issues
15(8)
1.9.1 Eliminating Missing Values
23(1)
1.10 Data Sets
23(2)
Chapter 2 A Foundation for Robust Methods
25(20)
2.1 Basic Tools for Judging Robustness
25(6)
2.1.1 Qualitative Robustness
26(3)
2.1.2 Infinitesimal Robustness
29(1)
2.1.3 Quantitative Robustness
30(1)
2.2 Some Measures of Location and Their Influence Function
31(7)
2.2.1 Quantiles
31(1)
2.2.2 The Winsorized Mean
32(2)
2.2.3 The Trimmed Mean
34(1)
2.2.4 M-Measures of Location
34(3)
2.2.5 R-Measures of Location
37(1)
2.3 Measures of Scale
38(2)
2.4 Scale Equivariant M-Measures of Location
40(1)
2.5 Winsorized Expected Values
41(4)
Chapter 3 Estimating Measures of Location and Scale
45(62)
3.1 A Bootstrap Estimate of a Standard Error
45(3)
3.1.1 R Function bootse
47(1)
3.2 Density Estimators
48(9)
3.2.1 Silverman's Rule of Thumb
49(1)
3.2.2 Rosenblatt's Shifted Histogram
49(1)
3.2.3 The Expected Frequency Curve
50(1)
3.2.4 An Adaptive Kernel Estimator
51(1)
3.2.5 R Functions skerd, kerSORT, kerden, kdplot, rdplot, akerd and splot
52(5)
3.3 The Sample Trimmed Mean
57(9)
3.3.1 R Functions mean, tmean and Hoc
59(1)
3.3.2 Estimating the Standard Error of the Trimmed Mean
60(4)
3.3.3 Estimating the Standard Error of the Sample Winsorized Mean
64(1)
3.3.4 R Functions winmean, winvar, trimse and winse
65(1)
3.3.5 Estimating the Standard Error of the Sample Median
65(1)
3.3.6 R Function msmedse
66(1)
3.4 The Finite Sample Breakdown Point
66(1)
3.5 Estimating Quantiles
67(6)
3.5.1 Estimating the Standard Error of the Sample Quantile
68(1)
3.5.2 R Function qse
69(1)
3.5.3 The Maritz--Jarrett Estimate of the Standard Error of xq
70(1)
3.5.4 R Function mjse
71(1)
3.5.5 The Harrell--Davis Estimator
71(1)
3.5.6 R Functions qest and hd
72(1)
3.5.7 A Bootstrap Estimate of the Standard Error of θq
73(1)
3.5.8 R Function hdseb
73(1)
3.6 An M-Estimator of Location
73(12)
3.6.1 R Function mad
78(1)
3.6.2 Computing an M-Estimator of Location
79(1)
3.6.3 R Functions mest
80(1)
3.6.4 Estimating the Standard Error of the M-Estimator
81(2)
3.6.5 R Function mestse
83(1)
3.6.6 A Bootstrap Estimate of the Standard Error of μm
84(1)
3.6.7 R Function mestseb
84(1)
3.7 One-Step M-Estimator
85(1)
3.7.1 R Function onestep
86(1)
3.8 W-Estimators
86(3)
3.8.1 Tau Measure of Location
87(1)
3.8.2 R Function tauloc
88(1)
3.8.3 Zuo's Weighted Estimator
88(1)
3.9 The Hodges--Lehmann Estimator
89(1)
3.10 Skipped Estimators
89(1)
3.10.1 R Functions mom and bmean
90(1)
3.11 Some Comparisons of the Location Estimators
90(3)
3.12 More Measures of Scale
93(7)
3.12.1 The Biweight Midvariance
94(2)
3.12.2 R Function bivar
96(1)
3.12.3 The Percentage Bend Midvariance and Tau Measure of Variation
96(2)
3.12.4 R Functions pbvar, tauvar
98(1)
3.12.5 The Interquartile Range
99(1)
3.12.6 R Functions idealf and idrange
99(1)
3.13 Some Outlier Detection Methods
100(5)
3.13.1 Rules Based on Means and Variances
100(1)
3.13.2 A Method Based on the Interquartile Range
101(1)
3.13.3 Carling's Modification
101(1)
3.13.4 A MAD-Median Rule
101(1)
3.13.5 R Functions outbox, out and boxplot
102(2)
3.13.6 R Functions adjboxout and adjbox
104(1)
3.14 Exercises
105(2)
Chapter 4 Confidence Intervals in the One-Sample Case
107(38)
4.1 Problems when Working with Means
107(4)
4.2 The g-and-h Distribution
111(4)
4.2.1 R Functions ghdist, rmul, rngh and ghtrim
114(1)
4.3 Inferences About the Trimmed and Winsorized Means
115(5)
4.3.1 R Functions trimci, winci and D.akp.effect
120(1)
4.4 Basic Bootstrap Methods
120(10)
4.4.1 The Percentile Bootstrap Method
121(1)
4.4.2 R Functions onesampb and hdpb
122(1)
4.4.3 Bootstrap-t Method
123(2)
4.4.4 Bootstrap Methods when Using a Trimmed Mean
125(4)
4.4.5 Singh's Modification
129(1)
4.4.6 R Functions trimpb and trimcibt
130(1)
4.5 Inferences About M-Estimators
130(3)
4.5.1 R Functions mestci and momci
132(1)
4.6 Confidence Intervals for Quantiles
133(7)
4.6.1 Beware of Tied Values when Making Inferences About Quantiles
136(1)
4.6.2 A Modification of the Distribution-Free Method for the Median
137(1)
4.6.3 R Functions qmjci, hdci, sint, sintv2, qci, qcipb and qint
138(2)
4.7 Empirical Likelihood
140(2)
4.7.1 Bartlett Corrected Empirical Likelihood
140(2)
4.8 Concluding Remarks
142(1)
4.9 Exercises
143(2)
Chapter 5 Comparing Two Croups
145(90)
5.1 The Shift Function
146(16)
5.1.1 The Kolmogorov-Smirnov Test
149(3)
5.1.2 R Functions ks, kssig, kswsig, and kstiesig
152(1)
5.1.3 The B and W Band for the Shift Function
153(2)
5.1.4 R Functions sband and wband
155(3)
5.1.5 Confidence Band for Specified Quantiles
158(2)
5.1.6 R Functions shifthd, qcomhd, qcomhdMC and q2gci
160(1)
5.1.7 R Functions g2plot and g5plot
161(1)
5.2 Student's t Test
162(4)
5.3 Comparing Medians and Other Trimmed Means
166(16)
5.3.1 R Functions yuen and msmed
169(1)
5.3.2 A Bootstrap-t Method for Comparing Trimmed Means
170(3)
5.3.3 R Functions yuenbt and yhbt
173(3)
5.3.4 Measuring Effect Size
176(4)
5.3.5 R Functions akp.effect, yuenv2, ees.ci, med.effect and qhat
180(2)
5.4 Inferences Based on a Percentile Bootstrap Method
182(5)
5.4.1 Comparing M-Estimators
183(1)
5.4.2 Comparing Trimmed Means and Medians
184(1)
5.4.3 R Functions trimpb2, pb2gen, m2ci, medpb2 and M2gbt
185(2)
5.5 Comparing Measures of Scale
187(2)
5.5.1 Comparing Variances
187(1)
5.5.2 R Function comvar2
188(1)
5.5.3 Comparing Biweight Midvariances
188(1)
5.5.4 R Function b2ci
189(1)
5.6 Permutation Tests
189(1)
5.6.1 R Function permg
190(1)
5.7 Rank-Based Methods and a Probabilistic Measure of Effect Size
190(8)
5.7.1 The Cliff and Brunner-Munzel Methods
192(3)
5.7.2 R Functions cid, cidv2, bmp, wmwloc, wmwpb and loc2plot
195(3)
5.8 Comparing Two Independent Binomial and Multinomial Distributions
198(7)
5.8.1 Storer--Kim Method
200(1)
5.8.2 Beal's Method
200(1)
5.8.3 KMS Method
201(1)
5.8.4 R Functions twobinom, twobici, bi2KMS, bi2KMSv2 and bi2CR
201(1)
5.8.5 Comparing Discrete (Multinomial) Distributions
202(1)
5.8.6 R Functions binband, splotg2, cumrelf
203(2)
5.9 Comparing Dependent Groups
205(27)
5.9.1 A Shift Function for Dependent Groups
206(1)
5.9.2 R Function lband
207(1)
5.9.3 Comparing Specified Quantiles
207(3)
5.9.4 R Functions shiftdhd, Dqcomhd, qdec2, Dqdif and difQpci
210(2)
5.9.5 Comparing Trimmed Means
212(3)
5.9.6 R Functions yuend, yuendv2 and D.akp.effect
215(2)
5.9.7 A Bootstrap-t Method for Marginal Trimmed Means
217(1)
5.9.8 R Function ydbt
217(1)
5.9.9 Inferences About the Distribution of Difference Scores
217(2)
5.9.10 R Functions loc2dif and 12drmci
219(1)
5.9.11 Percentile Bootstrap: Comparing Medians, M-Estimators and Other Measures of Location and Scale
220(1)
5.9.12 R Function bootdpci
221(1)
5.9.13 Handling Missing Values
222(4)
5.9.14 R Functions rm2miss and rmmismcp
226(1)
5.9.15 Comparing Variances
227(1)
5.9.16 R Function comdvar
228(1)
5.9.17 The Sign Test and Inferences About the Binomial Distribution
228(3)
5.9.18 R Functions binomci, acbinomci and binomLCO
231(1)
5.10 Exercises
232(3)
Chapter 6 Some Multivariate Methods
235(144)
6.1 Generalized Variance
235(1)
6.2 Depth
236(9)
6.2.1 Mahalanobis Depth
236(1)
6.2.2 Halfspace Depth
236(3)
6.2.3 Computing Halfspace Depth
239(2)
6.2.4 R Functions depth2, depth, fdepth, fdepthv2, unidepth
241(1)
6.2.5 Projection Depth
242(1)
6.2.6 R Functions pdis, pdisMC, and pdepth
243(1)
6.2.7 Other Measures of Depth
244(1)
6.2.8 R Functions zdist, zoudepth and prodepth
245(1)
6.3 Some Affine Equivariant Estimators
245(12)
6.3.1 Minimum Volume Ellipsoid Estimator
247(1)
6.3.2 The Minimum Covariance Determinant Estimator
247(1)
6.3.3 S-Estimators and Constrained M-Estimators
248(1)
6.3.4 R Function tbs
249(1)
6.3.5 Donoho--Gasko Generalization of a Trimmed Mean
249(1)
6.3.6 R Functions dmean and dcov
250(2)
6.3.7 The Stahel--Donoho W-Estimator
252(1)
6.3.8 R Function sdwe
253(1)
6.3.9 Median Ball Algorithm
253(1)
6.3.10 R Function rmba
253(1)
6.3.11 OGK Estimator
254(1)
6.3.12 R Function ogk
255(1)
6.3.13 An M-Estimator
255(1)
6.3.14 R Functions MARest and dmedian
256(1)
6.4 Multivariate Outlier Detection Methods
257(20)
6.4.1 A Relplot
258(2)
6.4.2 R Function relplot
260(1)
6.4.3 The MVE Method
260(1)
6.4.4 The MCD Method
261(1)
6.4.5 R Functions covmve and covmcd
261(1)
6.4.6 R Function out
262(1)
6.4.7 The MGV Method
263(2)
6.4.8 R Function outmgv
265(1)
6.4.9 A Projection Method
266(2)
6.4.10 R Functions outpro and out3d
268(1)
6.4.11 Outlier Identification in High Dimensions
269(1)
6.4.12 R Functions outproad and outmgvad
270(1)
6.4.13 Methods Designed for Functional Data
270(2)
6.4.14 R Functions FBplot, Flplot, medcurve, func.out, spag.plot, funloc and funlocpb
272(3)
6.4.15 Comments on Choosing a Method
275(2)
6.5 A Skipped Estimator of Location and Scatter
277(3)
6.5.1 R Functions smean, wmcd, wmve, mgvmean, L1 medcen, spat, mgvcov, skip, skipcov
278(2)
6.6 Robust Generalized Variance
280(1)
6.6.1 R Function gvarg
280(1)
6.7 Multivariate Location: Inference in the One-Sample Case
281(4)
6.7.1 Inferences Based on the OP Measure of Location
281(1)
6.7.2 Extension of Hotelling's T2 to Trimmed Means
282(1)
6.7.3 R Functions smeancrv2 and hotell.tr
283(1)
6.7.4 Inferences Based on the MGV Estimator
284(1)
6.7.5 R Function smgvcr
285(1)
6.8 Comparing OP Measures of Location
285(3)
6.8.1 R Functions smean2, matsplit and mat2grp
286(1)
6.8.2 Comparing Robust Generalized Variances
287(1)
6.8.3 R Function gvar2g
287(1)
6.9 Multivariate Density Estimators
288(1)
6.10 A Two-Sample, Projection-Type Extension of the Wilcoxon--Mann--Whitney Test
289(3)
6.10.1 R Functions mulwmw and mulwmwv2
291(1)
6.11 A Relative Depth Analog of the Wilcoxon--Mann--Whitney Test
292(4)
6.11.1 R Function mwmw
294(2)
6.12 Comparisons Based on Depth
296(4)
6.12.1 R Functions lsqs3 and depthg2
298(2)
6.13 Comparing Dependent Groups Based on All Pairwise Differences
300(2)
6.13.1 R Function dfried
302(1)
6.14 Robust Principal Components Analysis
302(11)
6.14.1 R Functions prcomp and regpca
304(1)
6.14.2 Maronna's Method
305(1)
6.14.3 The SPCA Method
305(1)
6.14.4 Method HRVB
306(1)
6.14.5 Method OP
306(1)
6.14.6 Method PPCA
307(1)
6.14.7 R Functions outpca, robpca, robpcas, SPCA, Ppca, Ppca, Summary
308(1)
6.14.8 Comments on Choosing the Number of Components
309(4)
6.15 Cluster Analysis
313(2)
6.15.1 R Functions Kmeans, kmeans.grp, TKmeans, TKmeans.grp
314(1)
6.16 Multivariate Discriminate Analysis
315(2)
6.16.1 R Function KNNdist
316(1)
6.17 Exercises
317(62)
Chapter 7 One-Way and Higher Designs for Independent Groups
379(98)
7.1 Trimmed Means and a One-Way Design
320(13)
7.1.1 A Welch-Type Procedure and a Robust Measure of Effect Size
321(2)
7.1.2 R Functions t1way, t1wayv2, esmcp, fac2list, t1wayF
323(4)
7.1.3 A Generalization of Box's Method
327(1)
7.1.4 R Function box 1 way
328(1)
7.1.5 Comparing Medians and Other Quantiles
328(2)
7.1.6 R Functions med 1 way and Qanova
330(1)
7.1.7 A Bootstrap-t Method
330(1)
7.1.8 R Functions t1waybt and btrim
331(2)
7.2 Two-Way Designs and Trimmed Means
333(8)
7.2.1 R Function t2way
337(2)
7.2.2 Comparing Medians
339(2)
7.2.3 R Functions med2way and Q2anova
341(1)
7.3 Three-Way Designs and Trimmed Means Including Medians
341(5)
7.3.1 R Functions t3way, fac2list and Q3anova
343(3)
7.4 Multiple Comparisons Based on Medians and Other Trimmed Means
346(26)
7.4.1 Basic Methods Based on Trimmed Means
347(2)
7.4.2 R Functions lincon, conCON and stepmcp
349(5)
7.4.3 Multiple Comparisons for Two-Way and Three-Way Designs
354(1)
7.4.4 R Functions bbmcp, mcp2med, bbbmcp, mcp3med, con2way and con3way
355(2)
7.4.5 A Bootstrap-t Procedure
357(2)
7.4.6 R Functions linconb, bbtrim and bbbtrim
359(2)
7.4.7 Controlling the Familywise Error Rate: Improvements on the Bonferroni Method
361(3)
7.4.8 R Functions p.adjust and mcpKadjp
364(1)
7.4.9 Percentile Bootstrap Methods for Comparing Medians, Other Trimmed Means and Quantiles
365(1)
7.4.10 R Functions linconpb, bbmcppb, bbbmcppb, medpb, Qmcp, med2mcp, med3mcp and q2by2
365(3)
7.4.11 Judging Sample Sizes
368(1)
7.4.12 R Function hochberg
369(1)
7.4.13 Explanatory Measure of Effect Size
370(1)
7.4.14 R Functions ESmainMCP and esImcp
370(1)
7.4.15 Comparing Curves (Functional Data)
371(1)
7.4.16 R Functions funyuenpb and Flplot2g
372(1)
7.5 A Random Effects Model for Trimmed Means
372(4)
7.5.1 A Winsorized Intraclass Correlation
373(3)
7.5.2 R Function rananova
376(1)
7.6 Global Tests Based on M-Measures of Location
376(9)
7.6.1 R Functions b1 way and pbadepth
380(1)
7.6.2 M-Estimators and Multiple Comparisons
381(3)
7.6.3 R Functions linconm and pbmcp
384(1)
7.6.4 M-Estimators and the Random Effects Model
385(1)
7.6.5 Other Methods for One-Way Designs
385(1)
7.7 M-Measures of Location and a Two-Way Design
385(4)
7.7.1 R Functions pbad2way and mcp2a
388(1)
7.8 Ranked-Based Methods for a One-Way Design
389(7)
7.8.1 The Rust--Fligner Method
389(2)
7.8.2 R Function rfanova
391(1)
7.8.3 A Heteroscedastic Rank-Based Method That Allows Tied Values
391(1)
7.8.4 R Function bdm
391(2)
7.8.5 Inferences About a Probabilistic Measure of Effect Size
393(2)
7.8.6 R Functions cidmulv2, wmwaov and cidM
395(1)
7.9 A Rank-Based Method for a Two-Way Design
396(4)
7.9.1 R Function bdm2way
397(1)
7.9.2 The Patel--Hoel Approach to Interactions
398(2)
7.9.3 R Function rimul
400(1)
7.10 MANOVA Based on Trimmed Means
400(9)
7.10.1 R Functions MULtr.anova, MULAOVp, bw2list and YYmanova
403(2)
7.10.2 Linear Contrasts
405(2)
7.10.3 R Functions linconMpb, linconSpb, YYmcp, fac2Mlist and fac2BBMlist
407(2)
7.11 Nested Designs
409(4)
7.11.1 R Functions anova.nestA, mcp.nestA and anova.nestAP
412(1)
7.12 Exercises
413(64)
Chapter 8 Comparing Multiple Dependent Croups
477(8)
8.1 Comparing Trimmed Means
417(9)
8.1.1 Omnibus Test Based on the Trimmed Means of the Marginal Distributions
418(1)
8.1.2 R Function rmanova
418(2)
8.1.3 Pairwise Comparisons and Linear Contrasts Based on Trimmed Means
420(3)
8.1.4 Linear Contrasts Based on the Marginal Random Variables
423(1)
8.1.5 R Functions rmmcp, rmmismcp and trimcimul
424(1)
8.1.6 Judging the Sample Size
424(2)
8.1.7 R Functions stein1.tr and stein2.tr
426(1)
8.2 Bootstrap Methods Based on Marginal Distributions
426(13)
8.2.1 Comparing Trimmed Means
427(1)
8.2.2 R Function rmanovab
427(1)
8.2.3 Multiple Comparisons Based on Trimmed Means
428(1)
8.2.4 R Functions pairdepb and bptd
429(2)
8.2.5 Percentile Bootstrap Methods
431(3)
8.2.6 R Functions bd 1 way, ddep and ddepGMC_C
434(2)
8.2.7 Multiple Comparisons Using M-Estimators or Skipped Estimators
436(1)
8.2.8 R Functions lindm and mcpOV
437(2)
8.3 Bootstrap Methods Based on Difference Scores
439(6)
8.3.1 R Function rmdzero
440(2)
8.3.2 Multiple Comparisons
442(1)
8.3.3 R Functions rmmcppb, wmcppb, dmedpb, lindepbt and qdmcpdif
443(2)
8.4 Comments on Which Method to Use
445(2)
8.5 Some Rank-Based Methods
447(2)
8.5.1 R Functions apanova and bprm
449(1)
8.6 Between-by-Within and Within-by-Within Designs
449(25)
8.6.1 Analyzing a Between-by-Within Design Based on Trimmed Means
449(2)
8.6.2 R Functions bwtrim and tsplit
451(3)
8.6.3 Data Management: R Function bw2list
454(1)
8.6.4 Bootstrap-t Method for a Between-by-Within Design
455(1)
8.6.5 R Functions bwtrimbt and tsplitbt
456(1)
8.6.6 Percentile Bootstrap Methods for a Between-by-Within Design
456(2)
8.6.7 R Functions sppba, sppbb and sppbi
458(1)
8.6.8 Multiple Comparisons
459(4)
8.6.9 R Functions bwmcp, bwamcp, bwbmcp, bwimcp, bwimcpES, spmcpa, spmcpb and spmcpi
463(2)
8.6.10 Within-by-Within Designs
465(1)
8.6.11 R Functions wwtrim, wwtrimbt, wwmcp, wwmcppb and wwmcpbt
466(1)
8.6.12 A Rank-Based Approach
467(3)
8.6.13 R Function bwrank
470(2)
8.6.14 Rank-Based Multiple Comparisons
472(1)
8.6.15 R Function bwrmcp
472(1)
8.6.16 Multiple Comparisons when Using a Patel--Hoel Approach to Interactions
473(1)
8.6.17 R Function sisplit
474(1)
8.7 Some Rank-Based Multivariate Methods
474(5)
8.7.1 The Munzel--Brunner Method
475(1)
8.7.2 R Function mulrank
476(1)
8.7.3 The Choi--Marden Multivariate Rank Test
477(2)
8.7.4 R Function cmanova
479(1)
8.8 Three-Way Designs
479(5)
8.8.1 Global Tests Based on Trimmed Means
480(1)
8.8.2 R Functions bbwtrim, bwwtrim, wwwtrim, bbwtrimbt, bwwtrimbt and wwwtrimbt
481(1)
8.8.3 Data Management: R Functions bw2list and bbw2list
481(1)
8.8.4 Multiple Comparisons
482(1)
8.8.5 R Function wwwmcp
483(1)
8.8.6 R Functions bbwmcp, bwwmcp, bbwmcppb, bwwmcppb and wwwmcppb
483(1)
8.9 Exercises
484(1)
Chapter 9 Correlation and Tests of Independence
485(32)
9.1 Problems with Pearson's Correlation
485(5)
9.1.1 Features of Data That Affect r and T
488(1)
9.1.2 Heteroscedasticity and the Classic Test that ρ = 0
489(1)
9.2 Two Types of Robust Correlations
490(1)
9.3 Some Type M Measures of Correlation
490(14)
9.3.1 The Percentage Bend Correlation
490(1)
9.3.2 A Test of Independence Based on ρpb
491(2)
9.3.3 R Function pbcor
493(1)
9.3.4 A Test of Zero Correlation Among p Random Variables
493(2)
9.3.5 R Function pball
495(1)
9.3.6 The Winsorized Correlation
496(1)
9.3.7 R Functions wincor and winall
497(1)
9.3.8 The Biweight Midcovariance and Correlation
498(1)
9.3.9 R Functions bicov and bicovm
499(1)
9.3.10 Kendall's tau
500(1)
9.3.11 Spearman's rho
501(1)
9.3.12 R Functions tau, spear, cor and taureg
502(1)
9.3.13 Heteroscedastic Tests of Zero Correlation
503(1)
9.3.14 R Functions corb, pcorb and pcorhc4
504(1)
9.4 Some Type O Correlations
504(5)
9.4.1 MVE and MCD Correlations
505(1)
9.4.2 Skipped Measures of Correlation
505(1)
9.4.3 The OP Correlation
505(1)
9.4.4 Inferences Based on Multiple Skipped Correlations
506(2)
9.4.5 R Functions scor, mscor and scorci
508(1)
9.5 A Test of Independence Sensitive to Curvature
509(4)
9.5.1 R Functions indt, indtall and medind
512(1)
9.6 Comparing Correlations: Independent Case
513(2)
9.6.1 Comparing Pearson Correlations
513(1)
9.6.2 Comparing Robust Correlations
514(1)
9.6.3 R Functions twopcor, twohc4cor and twocor
514(1)
9.7 Exercises
515(2)
Chapter 10 Robust Regression
517(68)
10.1 Problems with Ordinary Least Squares
518(12)
10.1.1 Computing Confidence Intervals Under Heteroscedasticity
521(5)
10.1.2 An Omnibus Test
526(1)
10.1.3 R Functions lsfitci, olshc4, hc4test and hc4wtest
527(2)
10.1.4 Comments on Comparing Means via Dummy Coding
529(1)
10.1.5 Salvaging the Homoscedasticity Assumption
529(1)
10.2 Theil--Sen Estimator
530(5)
10.2.1 R Functions tsreg, tshdreg, correg, regplot and regp2plot
533(2)
10.3 Least Median of Squares
535(1)
10.3.1 R Function lmsreg
535(1)
10.4 Least Trimmed Squares Estimator
535(1)
10.4.1 R Functions ltsreg and ltsgreg
536(1)
10.5 Least Trimmed Absolute Value Estimator
536(1)
10.5.1 R Function ltareg
537(1)
10.6 M-Estimators
537(1)
10.7 The Hat Matrix
538(3)
10.8 Generalized M-Estimators
541(4)
10.8.1 R Function bmreg
545(1)
10.9 The Coakley--Hettmansperger and Yohai Estimators
545(4)
10.9.1 MM-Estimator
547(1)
10.9.2 R Functions chreg and MMreg
548(1)
10.10 Skipped Estimators
549(1)
10.10.1 R Functions mgvreg and opreg
549(1)
10.11 Deepest Regression Line
550(1)
10.11.1 R Functions rdepth and mdepreg
551(1)
10.12 A Criticism of Methods with a High Breakdown Point
551(1)
10.13 Some Additional Estimators
551(14)
10.13.1 S-Estimators and τ-Estimators
552(1)
10.13.2 R Functions snmreg and stsreg
553(1)
10.13.3 E-Type Skipped Estimators
553(2)
10.13.4 R Functions mbmreg, tstsreg, tssnmreg and gyreg
555(1)
10.13.5 Methods Based on Robust Covariances
556(2)
10.13.6 R Functions bireg, winreg and COVreg
558(1)
10.13.7 L-Estimators
559(1)
10.13.8 L1 and Quantile Regression
559(1)
10.13.9 R Functions qreg, rqfit, qplotreg
560(1)
10.13.10 Methods Based on Estimates of the Optimal Weights
561(1)
10.13.11 Projection Estimators
562(1)
10.13.12 Methods Based on Ranks
562(2)
10.13.13 R Functions Rfit and Rfit.est
564(1)
10.13.14 Empirical Likelihood Type and Distance-Constrained Maximum Likelihood Estimators
565(1)
10.14 Comments About Various Estimators
565(6)
10.14.1 Contamination Bias
567(4)
10.15 Outlier Detection Based on a Robust Fit
571(2)
10.15.1 Detecting Regression Outliers
571(1)
10.15.2 R Functions reglev and rmblo
571(2)
10.16 Logistic Regression and the General Linear Model
573(4)
10.16.1 R Functions glm, logreg, wlogreg, logreg.plot
575(1)
10.16.2 The General Linear Model
576(1)
10.16.3 R Function glmrob
576(1)
10.17 Multivariate Regression
577(5)
10.17.1 The RADA Estimator
578(1)
10.17.2 The Least Distance Estimator
579(1)
10.17.3 R Functions MULMreg, mlrreg and Mreglde
579(2)
10.17.4 Multivariate Least Trimmed Squares Estimator
581(1)
10.17.5 R Function MULtsreg
581(1)
10.17.6 Other Robust Estimators
582(1)
10.18 Exercises
582(3)
Chapter 11 More Regression Methods
585(108)
11.1 Inferences About Robust Regression Parameters
585(21)
11.1.1 Omnibus Tests for Regression Parameters
586(4)
11.1.2 R Function regtest
590(1)
11.1.3 Inferences About Individual Parameters
591(2)
11.1.4 R Functions regci, regciMC and wlogregci
593(2)
11.1.5 Methods Based on the Quantile Regression Estimator
595(2)
11.1.6 R Functions rqtest, qregci and qrchk
597(1)
11.1.7 Inferences Based on the OP Estimator
598(2)
11.1.8 R Functions opregpb and opregpbMC
600(1)
11.1.9 Hypothesis Testing when Using a Multivariate Regression Estimator RADA
600(1)
11.1.10 R Function mlrGtest
601(1)
11.1.11 Robust ANOVA via Dummy Coding
601(1)
11.1.12 Confidence Bands for the Typical Value of y Given x
602(2)
11.1.13 R Functions regYhat, regYci, and regYband
604(2)
11.1.14 R Function regse
606(1)
11.2 Comparing the Regression Parameters of J ≥ 2 Groups
606(12)
11.2.1 Methods for Comparing Independent Groups
606(6)
11.2.2 R Functions reg2ci, reg1way, reg1wayISO, ancGpar, ols1way, ols1wayISO, olsJmcp, olsJ2, reg1mcp and olsWmcp
612(4)
11.2.3 Methods for Comparing Two Dependent Groups
616(2)
11.2.4 R Functions DregG, difreg, DregGOLS
618(1)
11.3 Detecting Heteroscedasticity
618(3)
11.3.1 A Quantile Regression Approach
619(1)
11.3.2 Koenker--Bassett Method
620(1)
11.3.3 R Functions qhomt and khomreg
620(1)
11.4 Curvature and Half-Slope Ratios
621(2)
11.4.1 R Function hratio
622(1)
11.5 Curvature and Nonparametric Regression
623(26)
11.5.1 Smoothers
624(1)
11.5.2 Kernel Estimators and Cleveland's LOWESS
624(2)
11.5.3 R Functions lplot, lplot.pred and kerreg
626(2)
11.5.4 The Running-Interval Smoother
628(5)
11.5.5 R Functions rplot and runYhat
633(2)
11.5.6 Smoothers for Estimating Quantiles
635(1)
11.5.7 R Function qhdsm
636(1)
11.5.8 Special Methods for Binary Outcomes
637(1)
11.5.9 R Functions logSM, logSMpred, bkreg and rplot.bin
638(1)
11.5.10 Smoothing with More than One Predictor
639(1)
11.5.11 R Functions rplot, runYhat, rplotsm and runpd
640(4)
11.5.12 LOESS
644(3)
11.5.13 Other Approaches
647(1)
11.5.14 R Functions adrun, adrunl, gamplot, gamplotINT
648(1)
11.6 Checking the Specification of a Regression Model
649(6)
11.6.1 Testing the Hypothesis of a Linear Association
650(1)
11.6.2 R Function lintest
651(1)
11.6.3 Testing the Hypothesis of a Generalized Additive Model
652(1)
11.6.4 R Function adtest
653(1)
11.6.5 Inferences About the Components of a Generalized Additive Model
653(1)
11.6.6 R Function adcom
654(1)
11.6.7 Detecting Heteroscedasticity Based on Residuals
654(1)
11.6.8 R Function rhom
655(1)
11.7 Regression Interactions and Moderator Analysis
655(9)
11.7.1 R Functions kercon, riplot, runsm2g, ols.plot.inter, olshc4.inter, reg.plot.inter and regci.inter
657(4)
11.7.2 Mediation Analysis
661(2)
11.7.3 R Functions ZYmediate, regmed2 and regmediate
663(1)
11.8 Comparing Parametric, Additive and Nonparametric Fits
664(2)
11.8.1 R Functions adpchk and pmodchk
664(2)
11.9 Measuring the Strength of an Association Given a Fit to the Data
666(5)
11.9.1 R Functions RobRsq, qcorp1 and qcor
669(1)
11.9.2 Comparing Two Independent Groups via the LOWESS Version of Explanatory Power
670(1)
11.9.3 R Functions smcorcom and smstrcom
671(1)
11.10 Comparing Predictors
671(16)
11.10.1 Comparing Correlations
672(3)
11.10.2 R Functions TWOpov, TWOpNOV, corCOMmcp, twoDcorR, and twoDNOV
675(1)
11.10.3 Methods Based on Prediction Error
676(2)
11.10.4 R Functions regpre and regpreCV
678(2)
11.10.5 R Function larsR
680(1)
11.10.6 Inferences About Which Predictors Are Best
681(5)
11.10.7 R Functions reglVcom, ts2str and sm2strv7
686(1)
11.11 Marginal Longitudinal Data Analysis: Comments on Comparing Groups
687(3)
11.11.1 R Functions long2g, longreg, longreg.plot and xyplot
689(1)
11.12 Exercises
690(3)
Chapter 12 ANCOVA
693(48)
12.1 Methods Based on Specific Design Points and a Linear Model
695(7)
12.1.1 Method S1
696(1)
12.1.2 Method S2
696(2)
12.1.3 Dealing with Two Covariates
698(1)
12.1.4 R Functions ancJN, ancJNmp, ancJNmpcp, anclin, reg2plot and reg2g.p2plot
699(3)
12.2 Methods when There Is Curvature and a Single Covariate
702(17)
12.2.1 Method Y
703(2)
12.2.2 Method BB: Bootstrap Bagging
705(1)
12.2.3 Method UB
706(1)
12.2.4 Method TAP
707(1)
12.2.5 Method G
708(2)
12.2.6 R Functions ancova, ancovaWMW, ancpb, rplot2g, runmean2g, lplot2g, ancdifplot, ancboot, ancbbpb, qhdsm2g, ancovaUB, ancovaUB.pv, ancdet, ancmg1 and ancGLOB
710(9)
12.3 Dealing with Two Covariates when There Is Curvature
719(12)
12.3.1 Method MC1
719(1)
12.3.2 Method MC2
720(2)
12.3.3 Method MC3
722(1)
12.3.4 R Functions ancovamp, ancovampG, ancmppb, ancmg, ancov2COV, ancdes and ancdet2C
723(8)
12.4 Some Global Tests
731(4)
12.4.1 Method TG
731(3)
12.4.2 R Functions ancsm and Qancsm
734(1)
12.5 Methods for Dependent Groups
735(5)
12.5.1 Methods Based on a Linear Model
735(1)
12.5.2 R Functions Dancts and Dancols
736(1)
12.5.3 Dealing with Curvature: Methods DY, DUB and DTAP
736(1)
12.5.4 R Functions Dancova, Dancovapb, DancovaUB and Dancdet
737(3)
12.6 Exercises
740(1)
References 741(38)
Index 779
Rand R. Wilcox has a Ph.D. in psychometrics, and is a professor of psychology at the University of Southern California. Wilcox's main research interests are statistical methods, particularly robust methods for comparing groups and studying associations. He also collaborates with researchers in occupational therapy, gerontology, biology, education and psychology. Wilcox is an internationally recognized expert in the field of Applied Statistics and has concentrated much of his research in the area of ANOVA and Regression. Wilcox is the author of 12 books on statistics and has published many papers on robust methods. He is currently an Associate Editor for four statistics journals and has served on many editorial boards. He has given numerous invited talks and workshops on robust methods.
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