Introduction to nonparametric estimation
- Alexandre B. Tsybakov.
- [English ed.].
- New York : Springer, c2009.
- Physical description
- xii, 214 p. : ill. ; 25 cm.
- Springer series in statistics.
Math & Statistics Library
|QA278.8 .T7913 2009||Unknown|
- Includes bibliographical references (p. -209) and index.
- Nonparametric estimators.- Lower bounds on the minimax risk.- Asymptotic efficiency and adaptation.- Appendix.- References.- Index.
- (source: Nielsen Book Data)9780387790510 20160528
- Publisher's Summary
- 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. This book will be useful for researchers and grad students interested in theoretical aspects of smoothing techniques. Many important and useful results on optimal and adaptive estimation are provided. As one of the leading mathematical statisticians working in nonparametrics, the author is an authority on the subject.
(source: Nielsen Book Data)9780387790510 20160528
- 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, AlexanderNazin, PhilippeRigollet, AngelikaRohde, andJonWellnerfortheir valuable remarks that helped to improve the text. I am grateful to Centre de Recherche en Economie et Statistique (CREST) and to Isaac Newton Ins- tute for Mathematical Sciences which provided an excellent environment for ?nishing 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 ?nite number of parameters goes back to Fisher. However, parametric models provide only an approximation, often imprecise, of the - derlying 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 smoo- ness.
(source: Nielsen Book Data)9781441927095 20160611
- Publication date
- Springer series in statistics
- "The French edition of this work that is the basis of this work that is the basis of this expanded edition was translated by Vladimir Zaiats."--P. [i].
- 9780387790510 (hbk.)
- 0387790519 (hbk.)
- 0387790527 (ebk.)
- 9780387790527 (ebk.)
- Publisher Number
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