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The theory of empirical processes provides valuable tools for the development of asymptotic theory in (non-parametric) statistical models, and possibly the unified treatment of a number of them. This book reveals the relation between the asymptotic behaviour of M-estimators and the complexity of parameter space. Virtually all results are proved using only elementary ideas developed within the book; there is minimal recourse to abstract theoretical results. To make the results concrete, a detailed treatment is presented for two important examples of M-estimation, namely maximum likelihood and least squares. The theory also covers estimation methods using penalties and sieves.Many illustrative examples are given, including the Grenander estimator, estimation of functions of bounded variation, smoothing splines, partially linear models, mixture models and image analysis.Graduate students and professionals in statistics, as well as those with an interest in applications to such areas as econometrics, medical statistics, etc., will welcome this treatment.
|AUTEUR||Sara Van De Geer|
|DATE DE PUBLICATION||2000-Mar-02|
|TAILLE DU FICHIER||1,92 MB|
|NOM DE FICHIER||Empirical Processes in M-Estimation.pdf|
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Empirical Processes: Lecture 17 Spring, 2010 Introduction to Empirical Processes and Semiparametric Inference Lecture 17: Z-Estimators Michael R. Kosorok, Ph.D. Professor and Chair of Biostatistics Professor of Statistics and Operations Research University of North Carolina-Chapel Hill 1. Empirical Processes: Lecture 17 Spring, 2010 Z-Estimators Recall from Section 2.2.5 that Z-estimators are ...