Efficient and Adaptive Estimation for Semiparametric Models

By: P. J. Bickel, Chris A. Klaassen, Peter J. Bickel

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Paperback | 1 June 1998 | Edition Number 1998

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This book deals with estimation in situations in which there is believed to be enough information to model parametrically some, but not all of the features of a data set. Such models have arisen in a wide context in recent years, and involve new nonlinear estimation procedures. Statistical models of this type are directly applicable to fields such as economics, epidemiology, and astronomy.

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List of Examples	p. ix
List of Figures	p. xv
Preface	p. xvii
Introduction
Preliminaries	p. 1
Problems and scope	p. 2
Examples	p. 5
Asymptotic Inference for (Finite-Dimensional) Parametric Models
Regular parametric models in the I.I.D. case	p. 11
Regular estimates of Euclidean parameters	p. 17
The information bound and the Hajek-Le Cam convolution and asymptotic minimax theorems	p. 23
Nuisance parameters, adaptation, and some geometry	p. 27
Construction of [square root]n-consistent and efficient estimates	p. 40
Information Bounds for Euclidean Parameters in Infinite-Dimensional Models
Introduction and overview	p. 46
Tangent spaces	p. 48
Information bounds via derivatives of functions: the nonparametric approach	p. 57
Information bound calculations via scores: the semiparametric approach	p. 70
Euclidean Parameters: Further Examples
Introduction: models	p. 83
Semiparametric group models	p. 88
Regression models	p. 103
Biased sampling models	p. 113
Mixture models	p. 125
Missing data models	p. 143
Transformation models	p. 153
Information Bounds for Infinite-Dimensional Parameters
Introduction	p. 176
Convolution theorems for regular estimates of infinite-dimensional parameters	p. 177
Examples	p. 191
Differentiability of functions	p. 201
The "calculus" of efficient score and influence operators	p. 210
Infinite-Dimensional Parameters: Further Examples
Introduction	p. 221
Constrained families	p. 221
Group models	p. 229
Biased sampling models	p. 240
Mixture models and models with monotonicity constraints	p. 261
Missing data and censoring	p. 271
Transformation models	p. 292
Construction of Estimates
Introduction	p. 298
M-estimates for Euclidean parameters	p. 301
Generalized M-estimates for Euclidean parameters	p. 309
GMC- and GM-estimates corresponding to convex D	p. 325
Estimation of P and other infinite-dimensional parameters: methods, consistency, and rates of convergence	p. 335
Estimation of infinite-dimensional parameters: asymptotics and applications	p. 356
Joint estimation of Euclidean and infinite-dimensional parameters	p. 382
Efficient estimation	p. 391
Appendix
Vector spaces; linear functionals and dual spaces	p. 414
Orthogonality and projection formulas	p. 425
Conditional expectation formulas	p. 430
Projection on sumspaces and ACE	p. 436
Derivatives	p. 453
Metrics on classes of probability measures and probability inequalities	p. 464
Limit theorems, weak convergence, and tightness	p. 468
Hoffmann-Jorgensen-Dudley weak convergence theory	p. 475
Contiguity	p. 498
The master theorem for asymptotic generalized M-estimates	p. 514
List of Symbols	p. 521
Bibliography	p. 527
Author Index	p. 549
Subject Index	p. 553
Table of Contents provided by Rittenhouse. All Rights Reserved.

Efficient and Adaptive Estimation for Semiparametric Models

At a Glance

Paperback

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