Springer Series in Statistics

Introduction to Nonparametric Estimation

Authors: Tsybakov, Alexandre B.

  • Concise and self-contained treatment of the theory
  • Thorough analysis of optimality and adaptivity issues
  • Detailed account on minimax lower bounds
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eBook 91,62 €
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  • ISBN 978-0-387-79052-7
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  • Immediate eBook download after purchase
Hardcover 114,39 €
price for Spain (gross)
  • ISBN 978-0-387-79051-0
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  • Usually dispatched within 3 to 5 business days.
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Softcover 114,39 €
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  • ISBN 978-1-4419-2709-5
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  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

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.

Reviews

From the reviews:

“The book is meant to be an introduction to the rich theory of nonparametric estimation through some simple models and examples. The detailed proofs given in the book will help the interested reader to understand the subject better. This well written book will be welcomed by all those interested in learning the presented concepts. The author should be complimented for a good treatise with detailed proofs of several important results in nonparametric estimation theory.” (Ravi Sreenivasan, Zentralblatt MATH, Vol. 1176, 2010)

“...A short and rigorous introduction to minimax results for estimators of densities and regression functions from independent observations. Each of the three chapters ends with a section containing detailed biographical notes and a section with exercises complementing and illustrating the main results. This book is an excellent introduction to the results and techniques of minimax estimation.” (Journal of the American Statistical Association, Vol. 105, No. 489)

“The potential reader of this book should be conversant with functional analysis and topology … . for a broad spectrum of mathematical statisticians, especially in the Continental Europe, this will be welcome as a good reading material. … attempts to formulate the basic theory of nonparametric functional estimation, including (i) construction of such estimators, (ii) their (asymptotic) statistical properties, (iii) optimality, in some sense, and (iv) adaptive estimation. The author contends to present the material … in a broad sense more acceptable to statisticians.” (Pranab K. Sen, International Statistical Review, Vol. 79 (2), 2011)


Table of contents (3 chapters)

  • Nonparametric estimators

    Tsybakov, Alexandre B.

    Pages 1-76

    Preview Buy Chapter 30,19 €
  • Lower bounds on the minimax risk

    Tsybakov, Alexandre B.

    Pages 77-135

    Preview Buy Chapter 30,19 €
  • Asymptotic efficiency and adaptation

    Tsybakov, Alexandre B.

    Pages 137-190

    Preview Buy Chapter 30,19 €

Buy this book

eBook 91,62 €
price for Spain (gross)
  • ISBN 978-0-387-79052-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 114,39 €
price for Spain (gross)
  • ISBN 978-0-387-79051-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 114,39 €
price for Spain (gross)
  • ISBN 978-1-4419-2709-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Nonparametric Estimation
Authors
Series Title
Springer Series in Statistics
Copyright
2009
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-79052-7
DOI
10.1007/b13794
Hardcover ISBN
978-0-387-79051-0
Softcover ISBN
978-1-4419-2709-5
Series ISSN
0172-7397
Edition Number
1
Number of Pages
X, 214
Topics