Data analysis and approximate models: model choice, location-scale, analysis of variance, nonparametric regression and image analysis

Introduction IntroductionApproximate Models Notation Two Modes of Statistical AnalysisTowards One Mode of Analysis Approximation, Randomness, Chaos, Determinism ApproximationA Concept of Approximation Approximation Approximating a Data Set by a Model Approximation Regions Functionals and EquivarianceRegularization and Optimality Metrics and DiscrepanciesStrong and Weak Topologies On Being (almost) Honest Simulations and Tables Degree of Approximation and p-values ScalesStability of Analysis The Choice of En(α, P) Independence Procedures, Approximation and VaguenessDiscrete Models The Empirical Density Metrics and Discrepancies The Total Variation Metric The Kullback-Leibler and Chi-Squared Discrepancies The Po(λ) ModelThe b(k, p) and nb(k, p) Models The Flying Bomb Data The Student Study Times Data OutliersOutliers, Data Analysis and Models Breakdown Points and Equivariance Identifying Outliers and Breakdown Outliers in Multivariate Data Outliers in Linear Regression Outliers in Structured Data The Location-Scale ProblemRobustness Efficiency and Regularization M-functionalsApproximation Intervals, Quantiles and Bootstrapping Stigler's Comparison of Eleven Location Functionals Based on Historical Data Sets An Attempt at an Automatic Procedure Multidimensional M-functionals The Analysis of Variance The One-Way TableThe Two-Way TableThe Three-Way and Higher TablesInteractions in the Presence of NoiseExamples Nonparametric Regression: Location A Definition of Approximation RegularizationRates of Convergence and Approximation Bands Choosing Smoothing ParametersJoint Approximation of Two or More SamplesInverse Problems Heterogeneous Noise Nonparametric Regression: Scale The Standard Model and a Concept of Approximation Piecewise Constant Scale and Local Approximation GARCH Segmentation The Taut String and Scale Smooth Scale Functions Comparison of the Four Methods Location and ScaleImage Analysis Two and Higher Dimensions The Approximation RegionLinear Programming and Related Methods Choosing Smoothing ParametersNonparametric Densities Introduction Approximation Regions and RegularizationThe Taut String Strategy for Densities Smoothing the Taut String ApproximationA Critique of Statistics Likelihood Bayesian Statistics Sufficient Statistics Efficiency Asymptotics Model Choice What Can Actually Be Estimated? BibliographyIndex.