Introduction to Nonparametric Estimation
Methods of nonparametric estimation are located at the core of modern statistical science. The aim of this book is to give a short but mathematically self-contained introduction to the theory of nonparametric estimation. The emphasis is on the constructio
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The French edition of this work that is the basis of this expanded edition was translated by Vladimir Zaiats.
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Alexandre B. Tsybakov
Introduction to Nonparametric Estimation
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Alexandre B. Tsybakov Laboratoire de Statistique of CREST 3, av. Pierre Larousse 92240 Malakoff France and LPMA University of Paris 6 4, Place Jussieu 75252 Paris France [email protected]
ISBN: 978-0-387-79051-0 DOI 10.1007/978-0-387-79052-7
e-ISBN: 978-0-387-79052-7
Library of Congress Control Number: 2008939894 Mathematics Subject Classification: 62G05, 62G07, 62G20 c Springer Science+Business Media, LLC 2009 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper springer.com
Preface to the English Edition
This is a revised and extended version of the French book. The main changes are in Chapter 1 where the former Section 1.3 is removed and the rest of the material is substantially revised. Sections 1.2.4, 1.3, 1.9, and 2.7.3 are new. Each chapter now has the bibliographic notes and contains the exercises section. I would like to thank Cristina Butucea, Alexander Goldenshluger, Stephan Huckenmann, Yuri Ingster, Iain Johnstone, Vladimir Koltchinskii, Alexander Korostelev, Oleg Lepski, Karim Lounici, Axel Munk, Boaz Nadler, Alexander Nazin, Philippe Rigollet, Angelika Rohde, and Jon Wellner for their valuable remarks that helped to improve the text. I am grateful to Centre de Recherche en Economie et Statistique (CREST) and to Isaac Newton Institute for Mathematical Sciences which provided an excellent environment for finishing the work on the book. My thanks also go to Vladimir Zaiats for his highly competent translation of the French original into English and to John Kimmel for being a very supportive and patient editor.
Alexandre Tsybakov Paris, June 2008
Preface to the French Edition
The tradition of considering the problem of statistical estimation as that of estimation of a finite number of parameters goes back to Fisher. However, parametric models provide only an approximation, often imprecise, of the underlying statistical structure. Statistical models that explain the data in a more consistent way are often more complex: Unknown elements in these models are, in general, some functions having certain properties of smoothness. The problem
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