Robust Asymptotic Statistics

Volume I

AvHelmut Rieder

Häftad, Engelska, 2012

Del i serien Springer Series in Statistics

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Beskrivning

1 To the king, my lord, from your servant Balasi : 2 ... Maybe the scribe who reads to the king did not understand . Functionals extend the parameter of the assumed ideal center model to neighborhoods of this model that contain the actual distri bution.

Produktinformation

Utgivningsdatum:2012-02-16
Mått:155 x 235 x 23 mm
Vikt:628 g
Format:Häftad
Språk:Engelska
Serie:Springer Series in Statistics
Antal sidor:390
Förlag:Springer-Verlag New York Inc.
ISBN:9781468406269

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Innehållsförteckning

1: Von Mises Functionals.- 1.1 General Remarks.- 1.2 Regular Differentiations.- 1.3 The Delta Method.- 1.4 M Estimates.- 1.5 Quantiles.- 1.6 L Estimates.- 2: Log Likelihoods.- 2.1 General Remarks.- 2.2 Contiguity and Asymptotic Normality.- 2.3 Differentiable Families.- 2.4 Linear Regression.- 3: Asymptotic Statistics.- 3.1 General Remarks.- 3.2 Convolution Representation.- 3.3 Minimax Estimation.- 3.4 Testing.- 4: Nonparametric Statistics.- 4.1 Introduction.- 4.2 The Nonparametric Setup.- 4.3 Statistics of Functionals.- 4.4 Restricted Tangent Space.- 5: Optimal Influence Curves.- 5.1 Introduction.- 5.2 Minimax Risk.- 5.3 Oscillation.- 5.4 Robust Asymptotic Tests.- 5.5 Minimax Risk and Oscillation.- 6: Stable Constructions.- 6.1 The Construction Problem.- 6.2 M Equations.- 6.3 Minimum Distance.- 6.4 One-Steps.- 7: Robust Regression.- 7.1 The Ideal Model.- 7.2 Regression Neighborhoods.- 7.3 Conditional Bias.- 7.4 Optimal Influence Curves.- 7.5 Least Favorable Contamination Curves.- 7.6 Equivariance Under Basis Change.- Appendix A: Weak Convergence of Measures.- A.1 Basic Notions.- A.2 Convergence of Integrals.- A.3 Smooth Empirical Process.- A.4 Square Integrable Empirical Process.- Appendix B: Some Functional Analysis.- B.1 A Few Facts.- B.2 Lagrange Multipliers.- B.2.1 Neyman—Pearson Lemma.- Appendix C: Complements.- C.1 Parametric Finite-Sample Results.- C.2 Some Technical Results.- C.2.1 Calculus.- C.2.2 Topology.- C.2.3 Matrices.