Robust Statistical Methods with R (Hardcover)

INTRODUCTIONMATHEMATICAL TOOLS OF ROBUSTNESSStatistical ModelIllustration on Statistical EstimationStatistical FunctionalFisher's ConsistencySome Distances of Probability MeasuresRelations between DistancesDifferentiable Statistical FunctionalsGateau DerivativeFrechet DerivativeHadamard (Compact) DerivativeLarge Sample Distribution of Empirical FunctionalComputation and Software NotesProblems and ComplementsBASIC CHARACTERISTICS OF ROBUSTNESSInfluence FunctionDiscretized Form of Influence FunctionQualitative RobustnessQuantitative Characteristics of Robustness Based on Influence FunctionMaximum BiasBreakdown PointTail-Behavior Measure of a Statistical EstimatorVariance of Asymptotic Normal DistributionProblems and ComplementsROBUST ESTIMATORS OF REAL PARAMETERIntroductionM-EstimatorsM-Estimator of Location ParameterFinite Sample Minimax Property of M-EstimatorMoment Convergence of M-EstimatorsStudentized M-EstimatorsL-EstimatorsSequential M- and L-EstimatorsR-EstimatorsNumerical IllustrationComputation and Software NotesProblems and ComplementsROBUST ESTIMATORS IN LINEAR MODELIntroductionLeast Squares MethodM-EstimatorsGM-EstimatorsS-Estimators and MM-EstimatorsL-Estimators, Regression QuantilesRegression Rank ScoresRobust Scale StatisticsEstimators with High Breakdown PointsOne-Step Versions of EstimatorsNumerical IllustrationsComputation and Software NotesProblems and ComplementsMULTIVARIATE LOCATION MODELIntroductionMultivariate M-Estimators of Location and ScatterHigh Breakdown Estimators of Multivariate Location and ScatterAdmissibility and ShrinkageNumerical Illustrations and Software NotesProblem and ComplementsSOME LARGE SAMPLE PROPERTIES OF ROBUST PROCEDURESIntroductionM-EstimatorsL-EstimatorsR-EstimatorsInterrelationships of M-, L-, and R-EstimatorsMinimaximally Robust EstimatorsProblems and ComplementsSOME GOODNESS-OF-FIT TESTSIntroductionTests of Normality of the Shapiro-Wilk Type with Nuisance Regression and Scale ParametersGoodness-of-Fit Tests for General Distribution with Nuisance Regression and ScaleNumerical IllustrationComputation and Software NotesAPPENDIX A: R SYSTEMBrief R OverviewREFERENCESSUBJECT INDEXAUTHOR INDEX