Introduction to Nonparametric Estimation [electronic resource] / by Alexandre B. Tsybakov.

By: Tsybakov, Alexandre B [author.]
Contributor(s): SpringerLink (Online service)
Material type: TextTextSeries: Springer Series in Statistics: Publisher: New York, NY : Springer New York, 2009Description: X, 214 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387790527Subject(s): Statistics | Mathematical statistics | Pattern recognition | Probabilities | Econometrics | Statistics | Statistical Theory and Methods | Probability and Statistics in Computer Science | Pattern Recognition | Econometrics | Signal, Image and Speech Processing | Probability Theory and Stochastic ProcessesAdditional physical formats: Printed edition:: No titleDDC classification: 519.5 LOC classification: QA276-280Online resources: Click here to access online
Contents:
Nonparametric estimators -- Lower bounds on the minimax risk -- Asymptotic efficiency and adaptation.
In: Springer eBooksSummary: 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.
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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.

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