Introduction to Robust Estimation and Hypothesis Testing

Preface
1 Introduction
	1.1 Problems with Assuming Normality
	1.2 Transformations
	1.3 The Influence Curve
	1.4 The Central Limit Theorem
	1.5 Is the ANOVA F Robust?
	1.6 Regression
	1.7 More Remarks
	1.8 R Software
	1.9 Some Data Management Issues
		1.9.1 Eliminating Missing Values
	1.10 Data Sets
2 A Foundation for Robust Methods
	2.1 Basic Tools for Judging Robustness
		2.1.1 Qualitative Robustness
		2.1.2 Infinitesimal Robustness
		2.1.3 Quantitative Robustness
	2.2 Some Measures of Location and Their Influence Function
		2.2.1 Quantiles
		2.2.2 The Winsorized Mean
		2.2.3 The Trimmed Mean
		2.2.4 M-Measures of Location
		2.2.5 R-Measures of Location
	2.3 Measures of Scale
	2.4 Scale Equivariant M-Measures of Location
	2.5 Winsorized Expected Values
3 Estimating Measures of Locationand Scale
	3.1 A Bootstrap Estimate of a Standard Error
		3.1.1 R Function bootse
	3.2 Density Estimators
		3.2.1 Silverman\'s Rule of Thumb
		3.2.2 Rosenblatt\'s Shifted Histogram
		3.2.3 The Expected Frequency Curve
		3.2.4 An Adaptive Kernel Estimator
		3.2.5 R Functions skerd, kerSORT, kerden, kdplot, rdplot, akerd and splot
	3.3 The Sample Trimmed Mean
		3.3.1 R Functions mean, tmean and lloc
		3.3.2 Estimating the Standard Error of the Trimmed Mean
		3.3.3 Estimating the Standard Error of the Sample Winsorized Mean
		3.3.4 R Functions winmean, winvar, trimse and winse
		3.3.5 Estimating the Standard Error of the Sample Median
		3.3.6 R Function msmedse
	3.4 The Finite Sample Breakdown Point
	3.5 Estimating Quantiles
		3.5.1 Estimating the Standard Error of the Sample Quantile
		3.5.2 R Function qse
		3.5.3 The Maritz-Jarrett Estimate of the Standard Error of xq
		3.5.4 R Function mjse
		3.5.5 The Harrell-Davis Estimator
		3.5.6 R Functions qest and hd
		3.5.7 A Bootstrap Estimate of the Standard Error of thetaq
		3.5.8 R Function hdseb
	3.6 An M-Estimator of Location
		3.6.1 R Function mad
		3.6.2 Computing an M-Estimator of Location
		3.6.3 R Functions mest
		3.6.4 Estimating the Standard Error of the M-Estimator
		3.6.5 R Function mestse
		3.6.6 A Bootstrap Estimate of the Standard Error of µm
		3.6.7 R Function mestseb
	3.7 One-Step M-Estimator
		3.7.1 R Function onestep
	3.8 W-Estimators
		3.8.1 Tau Measure of Location
		3.8.2 R Function tauloc
		3.8.3 Zuo\'s Weighted Estimator
	3.9 The Hodges-Lehmann Estimator
	3.10 Skipped Estimators
		3.10.1 R Functions mom and bmean
	3.11 Some Comparisons of the Location Estimators
	3.12 More Measures of Scale
		3.12.1 The Biweight Midvariance
		3.12.2 R Function bivar
		3.12.3 The Percentage Bend Midvariance and Tau Measure of Variation
		3.12.4 R Functions pbvar, tauvar
		3.12.5 The Interquartile Range
		3.12.6 R Functions idealf and idrange
	3.13 Some Outlier Detection Methods
		3.13.1 Rules Based on Means and Variances
		3.13.2 A Method Based on the Interquartile Range
		3.13.3 Carling\'s Modification
		3.13.4 A MAD-Median Rule
		3.13.5 R Functions outbox, out and boxplot
		3.13.6 R Functions adjboxout and adjbox
	3.14 Exercises
4 Confidence Intervals in theOne-Sample Case
	4.1 Problems when Working with Means
	4.2 The g-and-h Distribution
		Multivariate g-and-h Distributions
		4.2.1 R Functions ghdist, rmul, rngh and ghtrim
	4.3 Inferences About the Trimmed and Winsorized Means
		4.3.1 R Functions trimci, winci and D.akp.effect
	4.4 Basic Bootstrap Methods
		4.4.1 The Percentile Bootstrap Method
		4.4.2 R Functions onesampb and hdpb
		4.4.3 Bootstrap-t Method
		4.4.4 Bootstrap Methods when Using a Trimmed Mean
		4.4.5 Singh\'s Modification
		4.4.6 R Functions trimpb and trimcibt
	4.5 Inferences About M-Estimators
		4.5.1 R Functions mestci and momci
	4.6 Confidence Intervals for Quantiles
		4.6.1 Beware of Tied Values when Making Inferences About Quantiles
		4.6.2 A Modification of the Distribution-Free Method for the Median
		4.6.3 R Functions qmjci, hdci, sint, sintv2, qci, qcipb and qint
	4.7 Empirical Likelihood
		4.7.1 Bartlett Corrected Empirical Likelihood
	4.8 Concluding Remarks
	4.9 Exercises
5 Comparing Two Groups
	5.1 The Shift Function
		5.1.1 The Kolmogorov-Smirnov Test
		5.1.2 R Functions ks, kssig, kswsig, and kstiesig
		5.1.3 The B and W Band for the Shift Function
		5.1.4 R Functions sband and wband
		5.1.5 Confidence Band for Specified Quantiles
			Method Q1
			Method Q2
		5.1.6 R Functions shifthd, qcomhd, qcomhdMC and q2gci
		5.1.7 R Functions g2plot and g5plot
	5.2 Student\'s t Test
	5.3 Comparing Medians and Other Trimmed Means
		Yuen\'s Method
		Comparing Medians
		5.3.1 R Functions yuen and msmed
		5.3.2 A Bootstrap-t Method for Comparing Trimmed Means
		5.3.3 R Functions yuenbt and yhbt
		5.3.4 Measuring Effect Size
			A Standardized Difference
			Explanatory Power
			A Classification Perspective
			A Probabilistic Measure of Effect Size
		5.3.5 R Functions akp.effect, yuenv2, ees.ci, med.effect and qhat
	5.4 Inferences Based on a Percentile Bootstrap Method
		5.4.1 Comparing M-Estimators
		5.4.2 Comparing Trimmed Means and Medians
		5.4.3 R Functions trimpb2, pb2gen, m2ci, medpb2 and M2gbt
	5.5 Comparing Measures of Scale
		5.5.1 Comparing Variances
		5.5.2 R Function comvar2
		5.5.3 Comparing Biweight Midvariances
		5.5.4 R Function b2ci
	5.6 Permutation Tests
		5.6.1 R Function permg
	5.7 Rank-Based Methods and a Probabilistic Measure of Effect Size
		5.7.1 The Cliff and Brunner-Munzel Methods
			Cliff\'s Method
			Brunner-Munzel Method
		5.7.2 R Functions cid, cidv2, bmp, wmwloc, wmwpb and loc2plot
	5.8 Comparing Two Independent Binomial and Multinomial Distributions
		5.8.1 Storer-Kim Method
		5.8.2 Beal\'s Method
		5.8.3 KMS Method
		5.8.4 R Functions twobinom, twobici, bi2KMS, bi2KMSv2 and bi2CR
		5.8.5 Comparing Discrete (Multinomial) Distributions
		5.8.6 R Functions binband, splotg2, cumrelf
	5.9 Comparing Dependent Groups
		5.9.1 A Shift Function for Dependent Groups
		5.9.2 R Function lband
		5.9.3 Comparing Specified Quantiles
			Method D1
			Method D2
			Method D3
		5.9.4 R Functions shiftdhd, Dqcomhd, qdec2ci, Dqdif and difQpci
		5.9.5 Comparing Trimmed Means
		5.9.6 R Functions yuend, yuendv2 and D.akp.effect
		5.9.7 A Bootstrap-t Method for Marginal Trimmed Means
		5.9.8 R Function ydbt
		5.9.9 Inferences About the Distribution of Difference Scores
		5.9.10 R Functions loc2dif and l2drmci
		5.9.11 Percentile Bootstrap: Comparing Medians, M-Estimators and Other Measures of Location and Scale
		5.9.12 R Function bootdpci
		5.9.13 Handling Missing Values
			Method M1
			Method M2
			Method M3
			Comments on Choosing a Method
		5.9.14 R Functions rm2miss and rmmismcp
		5.9.15 Comparing Variances
		5.9.16 R Function comdvar
		5.9.17 The Sign Test and Inferences About the Binomial Distribution
		5.9.18 R Functions binomci, acbinomci and binomLCO
	5.10 Exercises
6 Some Multivariate Methods
	6.1 Generalized Variance
	6.2 Depth
		6.2.1 Mahalanobis Depth
		6.2.2 Halfspace Depth
		6.2.3 Computing Halfspace Depth
		6.2.4 R Functions depth2, depth, fdepth, fdepthv2, unidepth
		6.2.5 Projection Depth
		6.2.6 R Functions pdis, pdisMC, and pdepth
		6.2.7 Other Measures of Depth
		6.2.8 R Functions zdist, zoudepth and prodepth
	6.3 Some Affine Equivariant Estimators
		6.3.1 Minimum Volume Ellipsoid Estimator
		6.3.2 The Minimum Covariance Determinant Estimator
		6.3.3 S-Estimators and Constrained M-Estimators
		6.3.4 R Function tbs
		6.3.5 Donoho-Gasko Generalization of a Trimmed Mean
		6.3.6 R Functions dmean and dcov
		6.3.7 The Stahel-Donoho W-Estimator
		6.3.8 R Function sdwe
		6.3.9 Median Ball Algorithm
		6.3.10 R Function rmba
		6.3.11 OGK Estimator
		6.3.12 R Function ogk
		6.3.13 An M-Estimator
		6.3.14 R Functions MARest and dmedian
	6.4 Multivariate Outlier Detection Methods
		6.4.1 A Relplot
		6.4.2 R Function relplot
		6.4.3 The MVE Method
		6.4.4 The MCD Method
		6.4.5 R Functions covmve and covmcd
		6.4.6 R Function out
		6.4.7 The MGV Method
		6.4.8 R Function outmgv
		6.4.9 A Projection Method
		6.4.10 R Functions outpro and out3d
		6.4.11 Outlier Identification in High Dimensions
		6.4.12 R Functions outproad and outmgvad
		6.4.13 Methods Designed for Functional Data
		6.4.14 R Functions FBplot, Flplot, medcurve, func.out, spag.plot, funloc and funlocpb
		6.4.15 Comments on Choosing a Method
	6.5 A Skipped Estimator of Location and Scatter
		6.5.1 R Functions smean, wmcd, wmve, mgvmean, L1medcen, spat, mgvcov, skip, skipcov
	6.6 Robust Generalized Variance
		6.6.1 R Function gvarg
	6.7 Multivariate Location: Inference in the One-Sample Case
		6.7.1 Inferences Based on the OP Measure of Location
		6.7.2 Extension of Hotelling\'s T2 to Trimmed Means
		6.7.3 R Functions smeancrv2 and hotel1.tr
		6.7.4 Inferences Based on the MGV Estimator
		6.7.5 R Function smgvcr
	6.8 Comparing OP Measures of Location
		6.8.1 R Functions smean2, matsplit and mat2grp
			Data Management
		6.8.2 Comparing Robust Generalized Variances
		6.8.3 R Function gvar2g
	6.9 Multivariate Density Estimators
	6.10 A Two-Sample, Projection-Type Extension of the Wilcoxon-Mann-Whitney Test
		6.10.1 R Functions mulwmw and mulwmwv2
	6.11 A Relative Depth Analog of the Wilcoxon-Mann-Whitney Test
		6.11.1 R Function mwmw
	6.12 Comparisons Based on Depth
		6.12.1 R Functions lsqs3 and depthg2
	6.13 Comparing Dependent Groups Based on All Pairwise Differences
		6.13.1 R Function dfried
	6.14 Robust Principal Components Analysis
		6.14.1 R Functions prcomp and regpca
		6.14.2 Maronna\'s Method
		6.14.3 The SPCA Method
		6.14.4 Method HRVB
		6.14.5 Method OP
		6.14.6 Method PPCA
		6.14.7 R Functions outpca, robpca, robpcaS, SPCA, Ppca, Ppca.summary
		6.14.8 Comments on Choosing the Number of Components
	6.15 Cluster Analysis
		6.15.1 R Functions Kmeans, kmeans.grp, TKmeans, TKmeans.grp
	6.16 Multivariate Discriminate Analysis
		6.16.1 R Function KNNdist
	6.17 Exercises
7 One-Way and Higher Designs for Independent Groups
	7.1 Trimmed Means and a One-Way Design
		7.1.1 A Welch-Type Procedure and a Robust Measure of Effect Size
			A Robust, Heteroscedastic Measure of Effect Size
		7.1.2 R Functions t1way, t1wayv2, esmcp, fac2list, t1wayF
			Data Management
		7.1.3 A Generalization of Box\'s Method
		7.1.4 R Function box1way
		7.1.5 Comparing Medians and Other Quantiles
		7.1.6 R Functions med1way and Qanova
		7.1.7 A Bootstrap-t Method
		7.1.8 R Functions t1waybt and btrim
	7.2 Two-Way Designs and Trimmed Means
		7.2.1 R Function t2way
		7.2.2 Comparing Medians
		7.2.3 R Functions med2way and Q2anova
	7.3 Three-Way Designs and Trimmed Means Including Medians
		7.3.1 R Functions t3way, fac2list and Q3anova
	7.4 Multiple Comparisons Based on Medians and Other Trimmed Means
		7.4.1 Basic Methods Based on Trimmed Means
			A Step-Down Multiple Comparison Procedure
		7.4.2 R Functions lincon, conCON and stepmcp
		7.4.3 Multiple Comparisons for Two-Way and Three-Way Designs
		7.4.4 R Functions bbmcp, mcp2med, bbbmcp, mcp3med, con2way and con3way
		7.4.5 A Bootstrap-t Procedure
		7.4.6 R Functions linconb, bbtrim and bbbtrim
		7.4.7 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
		7.4.8 R Functions p.adjust and mcpKadjp
		7.4.9 Percentile Bootstrap Methods for Comparing Medians, Other Trimmed Means and Quantiles
		7.4.10 R Functions linconpb, bbmcppb, bbbmcppb, medpb, Qmcp, med2mcp, med3mcp and q2by2
		7.4.11 Judging Sample Sizes
		7.4.12 R Function hochberg
		7.4.13 Explanatory Measure of Effect Size
		7.4.14 R Functions ESmainMCP and esImcp
		7.4.15 Comparing Curves (Functional Data)
		7.4.16 R Functions funyuenpb and Flplot2g
	7.5 A Random Effects Model for Trimmed Means
		7.5.1 A Winsorized Intraclass Correlation
		7.5.2 R Function rananova
	7.6 Global Tests Based on M-Measures of Location
		Method SHB
		Method LSB
		7.6.1 R Functions b1way and pbadepth
		7.6.2 M-Estimators and Multiple Comparisons
			Variation of a Bootstrap-t Method
			A Percentile Bootstrap Method: Method SR
		7.6.3 R Functions linconm and pbmcp
		7.6.4 M-Estimators and the Random Effects Model
		7.6.5 Other Methods for One-Way Designs
	7.7 M-Measures of Location and a Two-Way Design
		7.7.1 R Functions pbad2way and mcp2a
	7.8 Ranked-Based Methods for a One-Way Design
		7.8.1 The Rust-Fligner Method
		7.8.2 R Function rfanova
		7.8.3 A Heteroscedastic Rank-Based Method That Allows Tied Values
		7.8.4 R Function bdm
		7.8.5 Inferences About a Probabilistic Measure of Effect Size
			Method CHMCP
			Method WMWAOV
			Method DBH
		7.8.6 R Functions cidmulv2, wmwaov and cidM
	7.9 A Rank-Based Method for a Two-Way Design
		7.9.1 R Function bdm2way
		7.9.2 The Patel-Hoel Approach to Interactions
		7.9.3 R Function rimul
	7.10 MANOVA Based on Trimmed Means
		7.10.1 R Functions MULtr.anova, MULAOVp, bw2list and YYmanova
		7.10.2 Linear Contrasts
		7.10.3 R Functions linconMpb, linconSpb, YYmcp, fac2Mlist and fac2BBMlist
			Data Management
	7.11 Nested Designs
		7.11.1 R Functions anova.nestA, mcp.nestA and anova.nestAP
	7.12 Exercises
8 Comparing Multiple Dependent Groups
	8.1 Comparing Trimmed Means
		8.1.1 Omnibus Test Based on the Trimmed Means of the Marginal Distributions
		8.1.2 R Function rmanova
		8.1.3 Pairwise Comparisons and Linear Contrasts Based on Trimmed Means
		8.1.4 Linear Contrasts Based on the Marginal Random Variables
		8.1.5 R Functions rmmcp, rmmismcp and trimcimul
		8.1.6 Judging the Sample Size
		8.1.7 R Functions stein1.tr and stein2.tr
	8.2 Bootstrap Methods Based on Marginal Distributions
		8.2.1 Comparing Trimmed Means
		8.2.2 R Function rmanovab
		8.2.3 Multiple Comparisons Based on Trimmed Means
		8.2.4 R Functions pairdepb and bptd
		8.2.5 Percentile Bootstrap Methods
			Method RMPB3
			Method RMPB4
			Missing Values
		8.2.6 R Functions bd1way, ddep and ddepGMC_C
		8.2.7 Multiple Comparisons Using M-Estimators or Skipped Estimators
		8.2.8 R Functions lindm and mcpOV
	8.3 Bootstrap Methods Based on Difference Scores
		8.3.1 R Function rmdzero
		8.3.2 Multiple Comparisons
		8.3.3 R Functions rmmcppb, wmcppb, dmedpb, lindepbt and qdmcpdif
	8.4 Comments on Which Method to Use
	8.5 Some Rank-Based Methods
		Method AP
		Method BPRM
		Decision Rule
		8.5.1 R Functions apanova and bprm
	8.6 Between-by-Within and Within-by-Within Designs
		8.6.1 Analyzing a Between-by-Within Design Based on Trimmed Means
		8.6.2 R Functions bwtrim and tsplit
		8.6.3 Data Management: R Function bw2list
		8.6.4 Bootstrap-t Method for a Between-by-Within Design
		8.6.5 R Functions bwtrimbt and tsplitbt
		8.6.6 Percentile Bootstrap Methods for a Between-by-Within Design
		8.6.7 R Functions sppba, sppbb and sppbi
		8.6.8 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
		8.6.9 R Functions bwmcp, bwamcp, bwbmcp, bwimcp, bwimcpES, spmcpa, spmcpb and spmcpi
		8.6.10 Within-by-Within Designs
		8.6.11 R Functions wwtrim, wwtrimbt, wwmcp, wwmcppb and wwmcpbt
		8.6.12 A Rank-Based Approach
		8.6.13 R Function bwrank
		8.6.14 Rank-Based Multiple Comparisons
		8.6.15 R Function bwrmcp
		8.6.16 Multiple Comparisons when Using a Patel-Hoel Approach to Interactions
		8.6.17 R Function sisplit
	8.7 Some Rank-Based Multivariate Methods
		8.7.1 The Munzel-Brunner Method
		8.7.2 R Function mulrank
		8.7.3 The Choi-Marden Multivariate Rank Test
		8.7.4 R Function cmanova
	8.8 Three-Way Designs
		8.8.1 Global Tests Based on Trimmed Means
		8.8.2 R Functions bbwtrim, bwwtrim, wwwtrim, bbwtrimbt, bwwtrimbt and wwwtrimbt
		8.8.3 Data Management: R Functions bw2list and bbw2list
		8.8.4 Multiple Comparisons
		8.8.5 R Function wwwmcp
		8.8.6 R Functions bbwmcp, bwwmcp, bbwmcppb, bwwmcppb and wwwmcppb
			Bootstrap-t Methods
			Percentile Bootstrap Methods
	8.9 Exercises
9 Correlation and Tests of Independence
	9.1 Problems with Pearson\'s Correlation
		9.1.1 Features of Data That Affect r and T
		9.1.2 Heteroscedasticity and the Classic Test that rho=0
	9.2 Two Types of Robust Correlations
	9.3 Some Type M Measures of Correlation
		9.3.1 The Percentage Bend Correlation
		9.3.2 A Test of Independence Based on rhopb
		9.3.3 R Function pbcor
		9.3.4 A Test of Zero Correlation Among p Random Variables
		9.3.5 R Function pball
		9.3.6 The Winsorized Correlation
		9.3.7 R Functions wincor and winall
		9.3.8 The Biweight Midcovariance and Correlation
		9.3.9 R Functions bicov and bicovm
		9.3.10 Kendall\'s tau
		9.3.11 Spearman\'s rho
		9.3.12 R Functions tau, spear, cor and taureg
		9.3.13 Heteroscedastic Tests of Zero Correlation
		9.3.14 R Functions corb, pcorb and pcorhc4
	9.4 Some Type O Correlations
		9.4.1 MVE and MCD Correlations
		9.4.2 Skipped Measures of Correlation
		9.4.3 The OP Correlation
		9.4.4 Inferences Based on Multiple Skipped Correlations
		9.4.5 R Functions scor, mscor and scorci
	9.5 A Test of Independence Sensitive to Curvature
		Method INDT
		Method MEDIND
		9.5.1 R Functions indt, indtall and medind
	9.6 Comparing Correlations: Independent Case
		9.6.1 Comparing Pearson Correlations
		9.6.2 Comparing Robust Correlations
		9.6.3 R Functions twopcor, twohc4cor and twocor
	9.7 Exercises
10 Robust Regression
	10.1 Problems with Ordinary Least Squares
		10.1.1 Computing Confidence Intervals Under Heteroscedasticity
			Method HC4WB-D
			Method HC4WB-C
		10.1.2 An Omnibus Test
		10.1.3 R Functions lsfitci, olshc4, hc4test and hc4wtest
		10.1.4 Comments on Comparing Means via Dummy Coding
		10.1.5 Salvaging the Homoscedasticity Assumption
	10.2 Theil-Sen Estimator
		10.2.1 R Functions tsreg, tshdreg, correg, regplot and regp2plot
	10.3 Least Median of Squares
		10.3.1 R Function lmsreg
	10.4 Least Trimmed Squares Estimator
		10.4.1 R Functions ltsreg and ltsgreg
	10.5 Least Trimmed Absolute Value Estimator
		10.5.1 R Function ltareg
	10.6 M-Estimators
	10.7 The Hat Matrix
	10.8 Generalized M-Estimators
		10.8.1 R Function bmreg
	10.9 The Coakley-Hettmansperger and Yohai Estimators
		10.9.1 MM-Estimator
		10.9.2 R Functions chreg and MMreg
	10.10 Skipped Estimators
		10.10.1 R Functions mgvreg and opreg
	10.11 Deepest Regression Line
		10.11.1 R Functions rdepth and mdepreg
	10.12 A Criticism of Methods with a High Breakdown Point
	10.13 Some Additional Estimators
		10.13.1 S-Estimators and tau-Estimators
		10.13.2 R Functions snmreg and stsreg
		10.13.3 E-Type Skipped Estimators
		10.13.4 R Functions mbmreg, tstsreg, tssnmreg and gyreg
		10.13.5 Methods Based on Robust Covariances
		10.13.6 R Functions bireg, winreg and COVreg
		10.13.7 L-Estimators
		10.13.8 L1 and Quantile Regression
		10.13.9 R Functions qreg, rqfit, qplotreg
		10.13.10 Methods Based on Estimates of the Optimal Weights
		10.13.11 Projection Estimators
		10.13.12 Methods Based on Ranks
		10.13.13 R Functions Rfit and Rfit.est
		10.13.14 Empirical Likelihood Type and Distance-Constrained Maximum Likelihood Estimators
	10.14 Comments About Various Estimators
		10.14.1 Contamination Bias
	10.15 Outlier Detection Based on a Robust Fit
		10.15.1 Detecting Regression Outliers
		10.15.2 R Functions reglev and rmblo
	10.16 Logistic Regression and the General Linear Model
		10.16.1 R Functions glm, logreg, wlogreg, logreg.plot
		10.16.2 The General Linear Model
		10.16.3 R Function glmrob
	10.17 Multivariate Regression
		10.17.1 The RADA Estimator
		10.17.2 The Least Distance Estimator
		10.17.3 R Functions MULMreg, mlrreg and Mreglde
		10.17.4 Multivariate Least Trimmed Squares Estimator
		10.17.5 R Function MULtsreg
		10.17.6 Other Robust Estimators
	10.18 Exercises
11 More Regression Methods
	11.1 Inferences About Robust Regression Parameters
		11.1.1 Omnibus Tests for Regression Parameters
		11.1.2 R Function regtest
		11.1.3 Inferences About Individual Parameters
		11.1.4 R Functions regci, regciMC and wlogregci
		11.1.5 Methods Based on the Quantile Regression Estimator
		11.1.6 R Functions rqtest, qregci and qrchk
		11.1.7 Inferences Based on the OP Estimator
		11.1.8 R Functions opregpb and opregpbMC
		11.1.9 Hypothesis Testing when Using a Multivariate Regression Estimator RADA
		11.1.10 R Function mlrGtest
		11.1.11 Robust ANOVA via Dummy Coding
		11.1.12 Confidence Bands for the Typical Value of y Given x
		11.1.13 R Functions regYhat, regYci, and regYband
		11.1.14 R Function regse
	11.2 Comparing the Regression Parameters of J >=2 Groups
		11.2.1 Methods for Comparing Independent Groups
			Methods Based on the Least Squares Regression Estimator
			Multiple Comparisons
			Methods Based on Robust Estimators
		11.2.2 R Functions reg2ci, reg1way, reg1wayISO, ancGpar, ols1way, ols1wayISO, olsJmcp, olsJ2, reg1mcp and olsWmcp
		11.2.3 Methods for Comparing Two Dependent Groups
			Methods Based on a Robust Estimator
			Methods Based on the Least Squares Estimator
		11.2.4 R Functions DregG, difreg, DregGOLS
	11.3 Detecting Heteroscedasticity
		11.3.1 A Quantile Regression Approach
		11.3.2 Koenker-Bassett Method
		11.3.3 R Functions qhomt and khomreg
	11.4 Curvature and Half-Slope Ratios
		11.4.1 R Function hratio
	11.5 Curvature and Nonparametric Regression
		11.5.1 Smoothers
		11.5.2 Kernel Estimators and Cleveland\'s LOWESS
			Kernel Smoothing
			Cleveland\'s LOWESS
		11.5.3 R Functions lplot, lplot.pred and kerreg
		11.5.4 The Running-Interval Smoother
		11.5.5 R Functions rplot and runYhat
		11.5.6 Smoothers for Estimating Quantiles
		11.5.7 R Function qhdsm
		11.5.8 Special Methods for Binary Outcomes
		11.5.9 R Functions logSM, logSMpred, bkreg and rplot.bin
		11.5.10 Smoothing with More than One Predictor
		11.5.11 R Functions rplot, runYhat, rplotsm and runpd
		11.5.12 LOESS
		11.5.13 Other Approaches
		11.5.14 R Functions adrun, adrunl, gamplot, gamplotINT
	11.6 Checking the Specification of a Regression Model
		11.6.1 Testing the Hypothesis of a Linear Association
		11.6.2 R Function lintest
		11.6.3 Testing the Hypothesis of a Generalized Additive Model
		11.6.4 R Function adtest
		11.6.5 Inferences About the Components of a Generalized Additive Model
		11.6.6 R Function adcom
		11.6.7 Detecting Heteroscedasticity Based on Residuals
		11.6.8 R Function rhom
	11.7 Regression Interactions and Moderator Analysis
		11.7.1 R Functions kercon, riplot, runsm2g, ols.plot.inter, olshc4.inter, reg.plot.inter and regci.inter
		11.7.2 Mediation Analysis
		11.7.3 R Functions ZYmediate, regmed2 and regmediate
	11.8 Comparing Parametric, Additive and Nonparametric Fits
		11.8.1 R Functions adpchk and pmodchk
	11.9 Measuring the Strength of an Association Given a Fit to the Data
		11.9.1 R Functions RobRsq, qcorp1 and qcor
		11.9.2 Comparing Two Independent Groups via the LOWESS Version of Explanatory Power
		11.9.3 R Functions smcorcom and smstrcom
	11.10 Comparing Predictors
		11.10.1 Comparing Correlations
		11.10.2 R Functions TWOpov, TWOpNOV, corCOMmcp, twoDcorR, and twoDNOV
		11.10.3 Methods Based on Prediction Error
			The 0.632 Estimator
			The Leave-One-Out Cross-Validation Method
		11.10.4 R Functions regpre and regpreCV
		11.10.5 R Function larsR
		11.10.6 Inferences About Which Predictors Are Best
			Method IBS
			Method BTS
			Method SM
		11.10.7 R Functions regIVcom, ts2str and sm2strv7
	11.11 Marginal Longitudinal Data Analysis: Comments on Comparing Groups
		11.11.1 R Functions long2g, longreg, longreg.plot and xyplot
	11.12 Exercises
12 ANCOVA
	12.1 Methods Based on Specific Design Points and a Linear Model
		12.1.1 Method S1
		12.1.2 Method S2
		12.1.3 Dealing with Two Covariates
		12.1.4 R Functions ancJN, ancJNmp, ancJNmpcp, anclin, reg2plot and reg2g.p2plot
	12.2 Methods when There Is Curvature and a Single Covariate
		12.2.1 Method Y
		12.2.2 Method BB: Bootstrap Bagging
		12.2.3 Method UB
		12.2.4 Method TAP
		12.2.5 Method G
		12.2.6 R Functions ancova, ancovaWMW, ancpb, rplot2g, runmean2g, lplot2g, ancdifplot, ancboot, ancbbpb, qhdsm2g, ancovaUB, ancovaUB.pv, ancdet, ancmg1 and ancGLOB
	12.3 Dealing with Two Covariates when There Is Curvature
		12.3.1 Method MC1
		12.3.2 Method MC2
		12.3.3 Method MC3
		12.3.4 R Functions ancovamp, ancovampG, ancmppb, ancmg, ancov2COV, ancdes and ancdet2C
	12.4 Some Global Tests
		12.4.1 Method TG
		12.4.2 R Functions ancsm and Qancsm
	12.5 Methods for Dependent Groups
		12.5.1 Methods Based on a Linear Model
		12.5.2 R Functions Dancts and Dancols
		12.5.3 Dealing with Curvature: Methods DY, DUB and DTAP
		12.5.4 R Functions Dancova, Dancovapb, DancovaUB and Dancdet
	12.6 Exercises
Index
References