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Original Essays | November 9, 2009

Jesse Bullington: IMG Abash'd the Devil Stood

0 comments By Jesse Bullington

I don't believe in evil. It's a word I use, certainly, because words are shortcuts and we all take the short way round from time to time, but that's... Continue »
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    The Sad Tale of the Brothers Grossbart

    Jesse Bullington

Cambridge Series in Statistical and Probabilistic Mathematics #6: Empirical Processes in M-estimation

by Sara Van De Geer

Synopses & Reviews

Publisher Comments:

The theory of empirical processes provides valuable tools for the development of asymptotic theory in (nonparametric) statistical models, and makes it possible to give a unified treatment of various models. This book reveals the relation between the asymptotic behavior of M-estimators and the complexity of parameter space, using entropy as a measure of complexity, presenting tools and methods to analyze nonparametric, and in some cases, semiparametric methods. Graduate students and professionals in statistics, as well as those interested in applications, e.g. to econometrics, medical statistics, etc., will welcome this treatment.

Synopsis:

This book deals with estimation methods in statistics, and treats various models in a unified way. Virtually all results are proved using only elementary ideas developed within the book; there is minimal recourse to abstract theoretical results. 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.

Synopsis:

Advanced text; estimation methods in statistics, e.g. least squares; lots of examples; minimal abstraction.
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Table of Contents

Preface; Reading guide; 1. Introduction; 2. Notations and definitions; 3. Uniform laws of large numbers; 4. First applications: consistency; 5. Increments of empirical processes; 6. Central limit theorems; 7. Rates of convergence for maximum likelihood estimators; 8. The non-i.i.d. case; 9. Rates of convergence for least squares estimators; 10. Penalties and sieves; 11. Some applications to semi-parametric models; 12. M-estimators; Appendix; References; Author index; Subject index; List of symbols.

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Product Details

ISBN:
9780521650021
Editor:
Gill, R.
Publisher:
Cambridge Bibles
Editor:
Gill, R.
Author:
Gill, R.
Author:
Van de Geer, Sara
Author:
Ripley, B. D.
Author:
van de Geer, Sara A.
Author:
Ross, S.
Author:
Sara A. van de Geer
Author:
Williams, D.
Author:
Geer, S. A. Van De
Author:
Stein, M.
Location:
Cambridge ;
Subject:
Statistics
Subject:
Econometrics
Subject:
Estimation theory
Subject:
Nonparametric statistics
Subject:
Limit theorems (Probability theory)
Subject:
Limit theorems
Subject:
Probability & Statistics - General
Edition Description:
Includes bibliographical references and indexes.
Series:
Cambridge Series in Statistical and Probabilistic Mathematics
Series Volume:
6
Publication Date:
January 2000
Binding:
Hardcover
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
Yes
Pages:
298
Dimensions:
10.44x7.18x.85 in. 1.53 lbs.
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