Introduction to Nonparametric Estimation

Alexandre B. Tsybakov

ISBN 10: 1441927093 / ISBN 13: 9781441927095

Verlag: Springer New York, Springer US, 2010

Beschreibung

Druck auf Anfrage Neuware - Printed after ordering - 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.

Bestandsnummer des Verkäufers 9781441927095

Bibliografische Details

• Titel: Introduction to Nonparametric Estimation
• Verlag: Springer New York, Springer US
• Erscheinungsjahr: 2010
• Sprache: Englisch
• ISBN-10: 1441927093
• ISBN-13: 9781441927095
• Einband: Taschenbuch
• Zustand: Neu

Über diesen Titel

Inhaltsangabe

This book will be a valuable reference for researchers in the eare of nonparametrics.

Von der hinteren Coverseite

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.