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AuthorRieder, Helmut. author
TitleRobust Asymptotic Statistics [electronic resource] / by Helmut Rieder
ImprintNew York, NY : Springer US, 1994
Connect tohttp://dx.doi.org/10.1007/978-1-4684-0624-5
Descript XXII, 390 p. online resource

SUMMARY

To follow


CONTENT

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 Neymanโ{128}{148}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


Mathematics Probabilities Mathematics Probability Theory and Stochastic Processes



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