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Introduction to Nonparametric Estimation
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Catalogue Information
Field name
Details
Dewey Class
519.5
Title
Introduction to Nonparametric Estimation (EB) / by Alexandre B. Tsybakov.
Author
Tsybakov, Alexandre B.
Other name(s)
SpringerLink (Online service)
Publication
New York, NY : Springer , 2009.
Physical Details
X, 214 pages : online resource.
Series
Springer Series in Statistics
0172-7397
ISBN
9780387790527
Note
"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."-- Page [i].
Summary Note
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.:
Contents note
Nonparametric estimators -- Lower bounds on the minimax risk -- Asymptotic efficiency and adaptation -- Appendix -- References -- Index.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site
http://dx.doi.org/10.1007/b13794
Links to Related Works
Subject References:
Distribution (Probability theory)
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Econometrics
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Estimation theory
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Mathematical Statistics
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Nonparametric statistics
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Optical pattern recognition
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Probability and Statistics in Computer Science
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Statistical Theory and Methods
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Statistics
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Authors:
Tsybakov, Alexandre B.
.
See Also:
Cybakov, Aleksandr B.
.
Cybakov, Aleksandr Borisovič
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Corporate Authors:
SpringerLink (Online service)
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Series:
Springer Series in Statistics
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Classification:
519.5
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