Applications of empirical process theory / Sara A. van de Geer.

Format:

Book

Author/Creator:

Geer, S. A. van de (Sara A.)

Contributor:

Lippincott Library Book Endowment Fund.

Series:

Cambridge series on statistical and probabilistic mathematics

Cambridge series in statistical and probabilistic mathematics

Language:

English

Subjects (All):

Nonparametric statistics.

Estimation theory.

Limit theorems (Probability theory).

Statistics, Nonparametric.

Medical Subjects:

Statistics, Nonparametric.

Physical Description:

xii, 286 pages ; 27 cm.

Other Title:

Empirical processes in M-estimation

Place of Publication:

Cambridge ; New York : Cambridge University Press, 2000.

Summary:

"The theory of empirical processes provides tools for the development of asymptotic theory in (non-parametric) statistical models, and possibly the unified treatment of a number of them. This book reveals the relation between the asymptotic behaviour of M-estimators and the complexity of parameter space. Virtually all results are proved using only elementary ideas developed within the book; there is minimal recourse to abstract theoretical results. To make the results concrete, a detailed treatment is presented for two important examples of M-estimation, namely maximum likelihood and least squares. The theory also covers estimation methods using penalties and sieves."

"Many illustrative examples are given, including the Grenander estimator, estimation of functions of bounded variation, smoothing splines, partially linear models, mixture models and image analysis." "For Graduate students and professionals in statistics, as well as those with an interest in applications to such areas as econometrics, medical statistics, etc."--Jacket.

Contents:

1. Introduction

2. Notation and Definitions

3. Uniform Laws of Large Numbers

4. First Applications: Consistency

5. Increments of Empirical Processes

6. Central Limit Theorems

7. Rates of Convergence for Maximum Likelihood Estimators

8. The Non-I.I.D. Case

9. Rates of Convergence for Least Squares Estimators

10. Penalties and Sieves

11. Some Applications to Semiparametric Models

12. M-Estimators.

Notes:

Includes bibliographical references and indexes.

Local Notes:

Acquired for the Penn Libraries with assistance from the Lippincott Library Book Endowment Fund.

ISBN:

9780521650021

052165002X

9780521123259

0521123259

OCLC:

40267450

Online:

Publisher description