INTRODUCTION TO NONPARAMETRIC ESTIMATION TSYBAKOV PDF

It seems that you're in Germany. We have a dedicated site for Germany. 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.

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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. Skip to main content Skip to table of contents.

Advertisement Hide. This service is more advanced with JavaScript available. Introduction to Nonparametric Estimation. Authors view affiliations Alexandre B. Front Matter Pages Nonparametric estimators. Pages Lower bounds on the minimax risk. Asymptotic efficiency and adaptation. Back Matter Pages About this book Introduction Methods of nonparametric estimation are located at the core of modern statistical science. Estimator Nonparametric regression adaptive estimation density estimation minimax lower bound oracle inequality.

Authors and affiliations Alexandre B. Tsybakov 1 1. Buy options.

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