Wilcox R. Introduction to Robust Estimation and Hypothesis Testing

4th edition. — New York: Academic Press, 2017. — 787 p.Сontents:Problems with Assuming Normality
Transformations
The Influence Curve
The Central Limit Theorem
Is the ANOVA F Robust?
Regression
More Remarks
R Software
Some Data Management Issues
Eliminating Missing Values
Data SetsA Foundation for Robust Methods
Basic Tools for Judging Robustness
Qualitative Robustness
Infinitesimal Robustness
Quantitative Robustness
Some Measures of Location and Their Influence Function
Quantiles
The Winsorized Mean
The Trimmed Mean
M-Measures of Location
R-Measures of Location
Measures of Scale
Scale Equivariant M-Measures of Location
Winsorized Expected ValuesIntroduction-to-Robust-Estimation-a
Estimating Measures of Locationand Scale
A Bootstrap Estimate of a Standard Error
R Function bootse
Density Estimators
Silverman's Rule of Thumb
Rosenblatt's Shifted Histogram
The Expected Frequency Curve
An Adaptive Kernel Estimator
R Functions skerd, kerSORT, kerden, kdplot, rdplot, akerd and splot
The Sample Trimmed Mean
R Functions mean, tmean and lloc
Estimating the Standard Error of the Trimmed Mean
Estimating the Standard Error of the Sample Winsorized Mean
R Functions winmean, winvar, trimse and winse
Estimating the Standard Error of the Sample Median
R Function msmedse
The Finite Sample Breakdown Point
Estimating Quantiles
Estimating the Standard Error of the Sample Quantile
R Function qse
The Maritz-Jarrett Estimate of the Standard Error of xq
R Function mjse
The Harrell-Davis Estimator
R Functions qest and hd
A Bootstrap Estimate of the Standard Error of thetaq
R Function hdseb
An M-Estimator of Location
R Function mad
Computing an M-Estimator of Location
R Functions mest
Estimating the Standard Error of the M-Estimator
R Function mestse
A Bootstrap Estimate of the Standard Error of µm
R Function mestseb
One-Step M-Estimator
R Function onestep
W-Estimators
Tau Measure of Location
R Function tauloc
Zuo's Weighted Estimator
The Hodges-Lehmann Estimator
Skipped Estimators
R Functions mom and bmean
Some Comparisons of the Location Estimators
More Measures of Scale
The Biweight Midvariance
R Function bivar
The Percentage Bend Midvariance and Tau Measure of Variation
R Functions pbvar, tauvar
The Interquartile Range
R Functions idealf and idrange
Some Outlier Detection Methods
Rules Based on Means and Variances
A Method Based on the Interquartile Range
Carling's Modification
A MAD-Median Rule
R Functions outbox, out and boxplot
R Functions adjboxout and adjbox
ExercisesConfidence Intervals in theOne-Sample Case
Problems when Working with Means
The g-and-h Distribution
Multivariate g-and-h Distributions
R Functions ghdist, rmul, rngh and ghtrim
Inferences About the Trimmed and Winsorized Means
R Functions trimci, winci and Dakpeffect
Basic Bootstrap Methods
The Percentile Bootstrap Method
R Functions onesampb and hdpb
Bootstrap-t Method
Bootstrap Methods when Using a Trimmed Mean
Singh's Modification
R Functions trimpb and trimcibt
Inferences About M-Estimators
R Functions mestci and momci
Confidence Intervals for Quantiles
Beware of Tied Values when Making Inferences About Quantiles
A Modification of the Distribution-Free Method for the Median
R Functions qmjci, hdci, sint, sintv, qci, qcipb and qint
Empirical Likelihood
Bartlett Corrected Empirical Likelihood
Concluding Remarks
ExercisesComparing Two Groups
The Shift Function
The Kolmogorov-Smirnov Test
R Functions ks, kssig, kswsig, and kstiesig
The B and W Band for the Shift Function
R Functions sband and wband
Confidence Band for Specified Quantiles
Method Q
Method Q
R Functions shifthd, qcomhd, qcomhdMC and qgci
R Functions gplot and gplot
Student's t Test
Comparing Medians and Other Trimmed Means
Yuen's Method
Comparing Medians
R Functions yuen and msmed
A Bootstrap-t Method for Comparing Trimmed Means
R Functions yuenbt and yhbt
Measuring Effect Size
A Standardized Difference
Explanatory Power
A Classification Perspective
A Probabilistic Measure of Effect Size
R Functions akpeffect, yuenv, eesci, medeffect and qhat
Inferences Based on a Percentile Bootstrap Method
Comparing M-Estimators
Comparing Trimmed Means and Medians
R Functions trimpb, pbgen, mci, medpb and Mgbt
Comparing Measures of Scale
Comparing Variances
R Function comvar
Comparing Biweight Midvariances
R Function bci
Permutation Tests
R Function permg
Rank-Based Methods and a Probabilistic Measure of Effect Size
The Cliff and Brunner-Munzel Methods
Cliff's Method
Brunner-Munzel Method
R Functions cid, cidv, BMP, wmwloc, wmwpb and locplot
Comparing Two Independent Binomial and Multinomial Distributions
Storer-Kim Method
Beal's Method
KMS Method
R Functions twobinom, twobici, biKMS, biKMSv and biCR
Comparing Discrete (Multinomial) Distributions
R Functions binband, splotg, cumrelf
Comparing Dependent Groups
A Shift Function for Dependent Groups
R Function lband
Comparing Specified Quantiles
Method D
Method D
Method D
R Functions shiftdhd, Dqcomhd, qdecci, Dqdif and difQpci
Comparing Trimmed Means
R Functions yuend, yuendv and Dakpeffect
A Bootstrap-t Method for Marginal Trimmed Means
R Function ydbt
Inferences About the Distribution of Difference Scores
R Functions locdif and ldrmci
Percentile Bootstrap: Comparing Medians, M-Estimators and Other Measures of Location and Scale
R Function bootdpci
Handling Missing Values
Method M
Method M
Method M
Comments on Choosing a Method
R Functions rmmiss and rmmismcp
Comparing Variances
R Function comdvar
The Sign Test and Inferences About the Binomial Distribution
R Functions binomci, acbinomci and binomLCO
ExercisesSome Multivariate Methods
Generalized Variance
Depth
Mahalanobis Depth
Halfspace Depth
Computing Halfspace Depth
R Functions depth, depth, fdepth, fdepthv, unidepth
Projection Depth
R Functions pdis, pdisMC, and pdepth
Other Measures of Depth
R Functions zdist, zoudepth and prodepth
Some Affine Equivariant Estimators
Minimum Volume Ellipsoid Estimator
The Minimum Covariance Determinant Estimator
S-Estimators and Constrained M-Estimators
R Function tbs
Donoho-Gasko Generalization of a Trimmed Mean
R Functions dmean and dcov
The Stahel-Donoho W-Estimator
R Function sdwe
Median Ball Algorithm
R Function rmba
OGK Estimator
R Function ogk
An M-Estimator
R Functions MARest and dmedian
Multivariate Outlier Detection Methods
A Relplot
R Function relplot
The MVE Method
The MCD Method
R Functions covmve and covmcd
R Function out
The MGV Method
R Function outmgv
A Projection Method
R Functions outpro and outd
Outlier Identification in High Dimensions
R Functions outproad and outmgvad
Methods Designed for Functional Data
R Functions FBplot, Flplot, medcurve, funcout, spagplot, funloc and funlocpb
Comments on Choosing a Method
A Skipped Estimator of Location and Scatter
R Functions smean, wmcd, wmve, mgvmean, Lmedcen, spat, mgvcov, skip, skipcov
Robust Generalized Variance
R Function gvarg
Multivariate Location: Inference in the One-Sample Case
Inferences Based on the OP Measure of Location
Extension of Hotelling's T to Trimmed Means
R Functions smeancrv and hoteltr
Inferences Based on the MGV Estimator
R Function smgvcr
Comparing OP Measures of Location
R Functions smean, matsplit and matgrp
Data Management
Comparing Robust Generalized Variances
R Function gvarg
Multivariate Density Estimators
A Two-Sample, Projection-Type Extension of the Wilcoxon-Mann-Whitney Test
R Functions mulwmw and mulwmwv
A Relative Depth Analog of the Wilcoxon-Mann-Whitney Test
R Function mwmw
Comparisons Based on Depth
R Functions lsqs and depthg
Comparing Dependent Groups Based on All Pairwise Differences
R Function dfried
Robust Principal Components Analysis
R Functions prcomp and regpca
Maronna's Method
The SPCA Method
Method HRVB
Method OP
Method PPCA
R Functions outpca, robpca, robpcaS, SPCA, Ppca, Ppcasummary
Comments on Choosing the Number of Components
Cluster Analysis
R Functions Kmeans, kmeansgrp, TKmeans, TKmeansgrp
Multivariate Discriminate Analysis
R Function KNNdist
ExercisesOne-Way and Higher Designs for Independent Groups
Trimmed Means and a One-Way Design
A Welch-Type Procedure and a Robust Measure of Effect Size
A Robust, Heteroscedastic Measure of Effect Size
R Functions tway, twayv, esmcp, faclist, twayF
Data Management
A Generalization of Box's Method
R Function boxway
Comparing Medians and Other Quantiles
R Functions medway and Qanova
A Bootstrap-t Method
R Functions twaybt and btrim
Two-Way Designs and Trimmed Means
R Function tway
Comparing Medians
R Functions medway and Qanova
Three-Way Designs and Trimmed Means Including Medians
R Functions tway, faclist and Qanova
Multiple Comparisons Based on Medians and Other Trimmed Means
Basic Methods Based on Trimmed Means
A Step-Down Multiple Comparison Procedure
R Functions lincon, conCON and stepmcp
Multiple Comparisons for Two-Way and Three-Way Designs
R Functions bbmcp, mcpmed, bbbmcp, mcpmed, conway and conway
A Bootstrap-t Procedure
R Functions linconb, bbtrim and bbbtrim
Controlling the Familywise Error Rate: Improvements on the Bonferroni Method
Rom's Method
Hochberg's Method
Hommel's Method
Benjamini-Hochberg Method
The k-FWER Procedures
R Functions padjust and mcpKadjp
Percentile Bootstrap Methods for Comparing Medians, Other Trimmed Means and Quantiles
R Functions linconpb, bbmcppb, bbbmcppb, medpb, Qmcp, medmcp, medmcp and qby
Judging Sample Sizes
R Function hochberg
Explanatory Measure of Effect Size
R Functions ESmainMCP and esImcp
Comparing Curves (Functional Data)
R Functions funyuenpb and Flplotg
A Random Effects Model for Trimmed Means
A Winsorized Intraclass Correlation
R Function rananova
Global Tests Based on M-Measures of Location
Method SHB
Method LSB
R Functions bway and pbadepth
M-Estimators and Multiple Comparisons
Variation of a Bootstrap-t Method
A Percentile Bootstrap Method: Method SR
R Functions linconm and pbmcp
M-Estimators and the Random Effects Model
Other Methods for One-Way Designs
M-Measures of Location and a Two-Way Design
R Functions pbadway and mcpa
Ranked-Based Methods for a One-Way Design
The Rust-Fligner Method
R Function rfanova
A Heteroscedastic Rank-Based Method That Allows Tied Values
R Function bdm
Inferences About a Probabilistic Measure of Effect Size
Method CHMCP
Method WMWAOV
Method DBH
R Functions cidmulv, wmwaov and cidM
A Rank-Based Method for a Two-Way Design
R Function bdmway
The Patel-Hoel Approach to Interactions
R Function rimul
MANOVA Based on Trimmed Means
R Functions MULtranova, MULAOVp, bwlist and YYmanova
Linear Contrasts
R Functions linconMpb, linconSpb, YYmcp, facMlist and facBBMlist
Data Management
Nested Designs
R Functions anovanestA, mcpnestA and anovanestAP
ExercisesComparing Multiple Dependent Groups
Comparing Trimmed Means
Omnibus Test Based on the Trimmed Means of the Marginal Distributions
R Function rmanova
Pairwise Comparisons and Linear Contrasts Based on Trimmed Means
Linear Contrasts Based on the Marginal Random Variables
R Functions rmmcp, rmmismcp and trimcimul
Judging the Sample Size
R Functions steintr and steintr
Bootstrap Methods Based on Marginal Distributions
Comparing Trimmed Means
R Function rmanovab
Multiple Comparisons Based on Trimmed Means
R Functions pairdepb and bptd
Percentile Bootstrap Methods
Method RMPB
Method RMPB
Missing Values
R Functions bdway, ddep and ddepGMC_C
Multiple Comparisons Using M-Estimators or Skipped Estimators
R Functions lindm and mcpOV
Bootstrap Methods Based on Difference Scores
R Function rmdzero
Multiple Comparisons
R Functions rmmcppb, wmcppb, dmedpb, lindepbt and qdmcpdif
Comments on Which Method to Use
Some Rank-Based Methods
Method AP
Method BPRM
Decision Rule
R Functions apanova and bprm
Between-by-Within and Within-by-Within Designs
Analyzing a Between-by-Within Design Based on Trimmed Means
R Functions bwtrim and tsplit
Data Management: R Function bwlist
Bootstrap-t Method for a Between-by-Within Design
R Functions bwtrimbt and tsplitbt
Percentile Bootstrap Methods for a Between-by-Within Design
R Functions sppba, sppbb and sppbi
Multiple Comparisons
Method BWMCP
Method BWAMCP: Comparing Levels of Factor A for Each Level of Factor B
Method BWBMCP: Dealing with Factor B
Method BWIMCP: Interactions
Methods SPMCPA, SPMCPB and SPMCPI
R Functions bwmcp, bwamcp, bwbmcp, bwimcp, bwimcpES, spmcpa, spmcpb and spmcpi
Within-by-Within Designs
R Functions wwtrim, wwtrimbt, wwmcp, wwmcppb and wwmcpbt
A Rank-Based Approach
R Function bwrank
Rank-Based Multiple Comparisons
R Function bwrmcp
Multiple Comparisons when Using a Patel-Hoel Approach to Interactions
R Function sisplit
Some Rank-Based Multivariate Methods
The Munzel-Brunner Method
R Function mulrank
The Choi-Marden Multivariate Rank Test
R Function cmanova
Three-Way Designs
Global Tests Based on Trimmed Means
R Functions bbwtrim, bwwtrim, wwwtrim, bbwtrimbt, bwwtrimbt and wwwtrimbt
Data Management: R Functions bwlist and bbwlist
Multiple Comparisons
R Function wwwmcp
R Functions bbwmcp, bwwmcp, bbwmcppb, bwwmcppb and wwwmcppb
Bootstrap-t Methods
Percentile Bootstrap Methods
ExercisesCorrelation and Tests of Independence
Problems with Pearson's Correlation
Features of Data That Affect r and T
Heteroscedasticity and the Classic Test that rho=
Two Types of Robust Correlations
Some Type M Measures of Correlation
The Percentage Bend Correlation
A Test of Independence Based on rhopb
R Function pbcor
A Test of Zero Correlation Among p Random Variables
R Function pball
The Winsorized Correlation
R Functions wincor and winall
The Biweight Midcovariance and Correlation
R Functions bicov and bicovm
Kendall's tau
Spearman's rho
R Functions tau, spear, cor and taureg
Heteroscedastic Tests of Zero Correlation
R Functions corb, pcorb and pcorhc
Some Type O Correlations
MVE and MCD Correlations
Skipped Measures of Correlation
The OP Correlation
Inferences Based on Multiple Skipped Correlations
R Functions scor, mscor and scorci
A Test of Independence Sensitive to Curvature
Method INDT
Method MEDIND
R Functions indt, indtall and medind
Comparing Correlations: Independent Case
Comparing Pearson Correlations
Comparing Robust Correlations
R Functions twopcor, twohccor and twocor
ExercisesRobust Regression
Problems with Ordinary Least Squares
Computing Confidence Intervals Under Heteroscedasticity
Method HCWB-D
Method HCWB-C
An Omnibus Test
R Functions lsfitci, olshc, hctest and hcwtest
Comments on Comparing Means via Dummy Coding
Salvaging the Homoscedasticity Assumption
Theil-Sen Estimator
R Functions tsreg, tshdreg, correg, regplot and regpplot
Least Median of Squares
R Function lmsreg
Least Trimmed Squares Estimator
R Functions ltsreg and ltsgreg
Least Trimmed Absolute Value Estimator
R Function ltareg
M-Estimators
The Hat Matrix
Generalized M-Estimators
R Function bmreg
The Coakley-Hettmansperger and Yohai Estimators
MM-Estimator
R Functions chreg and MMreg
Skipped Estimators
R Functions mgvreg and opreg
Deepest Regression Line
R Functions rdepth and mdepreg
A Criticism of Methods with a High Breakdown Point
Some Additional Estimators
S-Estimators and tau-Estimators
R Functions snmreg and stsreg
E-Type Skipped Estimators
R Functions mbmreg, tstsreg, tssnmreg and gyreg
Methods Based on Robust Covariances
R Functions bireg, winreg and COVreg
L-Estimators
L and Quantile Regression
R Functions qreg, rqfit, qplotreg
Methods Based on Estimates of the Optimal Weights
Projection Estimators
Methods Based on Ranks
R Functions Rfit and Rfitest
Empirical Likelihood Type and Distance-Constrained Maximum Likelihood Estimators
Comments About Various Estimators
Contamination Bias
Outlier Detection Based on a Robust Fit
Detecting Regression Outliers
R Functions reglev and rmblo
Logistic Regression and the General Linear Model
R Functions glm, logreg, wlogreg, logregplot
The General Linear Model
R Function glmrob
Multivariate Regression
The RADA Estimator
The Least Distance Estimator
R Functions MULMreg, mlrreg and Mreglde
Multivariate Least Trimmed Squares Estimator
R Function MULtsreg
Other Robust Estimators
ExercisesMore Regression Methods
Inferences About Robust Regression Parameters
Omnibus Tests for Regression Parameters
R Function regtest
Inferences About Individual Parameters
R Functions regci, regciMC and wlogregci
Methods Based on the Quantile Regression Estimator
R Functions rqtest, qregci and qrchk
Inferences Based on the OP Estimator
R Functions opregpb and opregpbMC
Hypothesis Testing when Using a Multivariate Regression Estimator RADA
R Function mlrGtest
Robust ANOVA via Dummy Coding
Confidence Bands for the Typical Value of y Given x
R Functions regYhat, regYci, and regYband
R Function regse
Comparing the Regression Parameters of J >= Groups
Methods for Comparing Independent Groups
Methods Based on the Least Squares Regression Estimator
Multiple Comparisons
Methods Based on Robust Estimators
R Functions regci, regway, regwayISO, ancGpar, olsway, olswayISO, olsJmcp, olsJ, regmcp and olsWmcp
Methods for Comparing Two Dependent Groups
Methods Based on a Robust Estimator
Methods Based on the Least Squares Estimator
R Functions DregG, difreg, DregGOLS
Detecting Heteroscedasticity
A Quantile Regression Approach
Koenker-Bassett Method
R Functions qhomt and khomreg
Curvature and Half-Slope Ratios
R Function hratio
Curvature and Nonparametric Regression
Smoothers
Kernel Estimators and Cleveland's LOWESS
Kernel Smoothing
Cleveland's LOWESS
R Functions lplot, lplotpred and kerreg
The Running-Interval Smoother
R Functions rplot and runYhat
Smoothers for Estimating Quantiles
R Function qhdsm
Special Methods for Binary Outcomes
R Functions logSM, logSMpred, bkreg and rplotbin
Smoothing with More than One Predictor
R Functions rplot, runYhat, rplotsm and runpd
LOESS
Other Approaches
R Functions adrun, adrunl, gamplot, gamplotINT
Checking the Specification of a Regression Model
Testing the Hypothesis of a Linear Association
R Function lintest
Testing the Hypothesis of a Generalized Additive Model
R Function adtest
Inferences About the Components of a Generalized Additive Model
R Function adcom
Detecting Heteroscedasticity Based on Residuals
R Function rhom
Regression Interactions and Moderator Analysis
R Functions kercon, riplot, runsmg, olsplotinter, olshcinter, regplotinter and regciinter
Mediation Analysis
R Functions ZYmediate, regmed and regmediate
Comparing Parametric, Additive and Nonparametric Fits
R Functions adpchk and pmodchk
Measuring the Strength of an Association Given a Fit to the Data
R Functions RobRsq, qcorp and qcor
Comparing Two Independent Groups via the LOWESS Version of Explanatory Power
R Functions smcorcom and smstrcom
Comparing Predictors
Comparing Correlations
R Functions TWOpov, TWOpNOV, corCOMmcp, twoDcorR, and twoDNOV
Methods Based on Prediction Error
The Estimator
The Leave-One-Out Cross-Validation Method
R Functions regpre and regpreCV
R Function larsR
Inferences About Which Predictors Are Best
Method IBS
Method BTS
Method SM
R Functions regIVcom, tsstr and smstrv
Marginal Longitudinal Data Analysis: Comments on Comparing Groups
R Functions longg, longreg, longregplot and xyplot
ExercisesANCOVA
Methods Based on Specific Design Points and a Linear Model
Method S
Method S
Dealing with Two Covariates
R Functions ancJN, ancJNmp, ancJNmpcp, anclin, regplot and reggpplot
Methods when There Is Curvature and a Single Covariate
Method Y
Method BB: Bootstrap Bagging
Method UB
Method TAP
Method G
R Functions ancova, ancovaWMW, ancpb, rplotg, runmeang, lplotg, ancdifplot, ancboot, ancbbpb, qhdsmg, ancovaUB, ancovaUBpv, ancdet, ancmg and ancGLOB
Dealing with Two Covariates when There Is Curvature
Method MC
Method MC
Method MC
R Functions ancovamp, ancovampG, ancmppb, ancmg, ancovCOV, ancdes and ancdetC
Some Global Tests
Method TG
R Functions ancsm and Qancsm
Methods for Dependent Groups
Methods Based on a Linear Model
R Functions Dancts and Dancols
Dealing with Curvature: Methods DY, DUB and DTAP
R Functions Dancova, Dancovapb, DancovaUB and Dancdet
Exercises