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＜電子ブック＞
Introduction to Nonparametric Estimation / by Alexandre B. Tsybakov
(Springer Series in Statistics. ISSN:2197568X)

版	1st ed. 2009.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2009
本文言語	英語
大きさ	X, 214 p : online resource
著者標目	*Tsybakov, Alexandre B author SpringerLink (Online service)
件　名	LCSH:Statistics  LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Mathematical statistics LCSH:Pattern recognition systems LCSH:Econometrics LCSH:Signal processing LCSH:Probabilities FREE:Statistical Theory and Methods FREE:Probability and Statistics in Computer Science FREE:Automated Pattern Recognition FREE:Econometrics FREE:Signal, Speech and Image Processing FREE:Probability Theory
一般注記	Nonparametric estimators -- Lower bounds on the minimax risk -- Asymptotic efficiency and adaptation 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 construction of optimal estimators; therefore the concepts of minimax optimality and adaptivity, as well as the oracle approach, occupy the central place in the book. This is a concise text developed from lecture notes and ready to be used for a course on the graduate level. The main idea is to introduce the fundamental concepts of the theory while maintaining the exposition suitable for a first approach in the field. Therefore, the results are not always given in the most general form but rather under assumptions that lead to shorter or more elegant proofs. The book has three chapters. Chapter 1 presents basic nonparametric regression and density estimators and analyzes their properties. Chapter 2 is devoted to a detailed treatment of minimax lower bounds. Chapter 3 develops more advanced topics: Pinsker's theorem, oracle inequalities, Stein shrinkage, and sharp minimax adaptivity HTTP:URL=https://doi.org/10.1007/b13794

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