Synopses & Reviews
The theory of empirical processes provides valuable tools for the development of asymptotic theory in (nonparametric) statistical models, and makes it possible to give a unified treatment of various models. This book reveals the relation between the asymptotic behavior of M-estimators and the complexity of parameter space, using entropy as a measure of complexity, presenting tools and methods to analyze nonparametric, and in some cases, semiparametric methods. Graduate students and professionals in statistics, as well as those interested in applications, e.g. to econometrics, medical statistics, etc., will welcome this treatment.
'... well written and provides a modern contribution to a very important class of nonparametric estimators.' N. D. C. Veraverbeke, Publication of the International Statistical Institute
'... this excellent book will be extremely useful for graduate students and researchers in the general area of nonparametric estimation. It is a welcome addition to the existing literature and certainly recommended.' Niew Archief voor Wiskunde
Advanced text; estimation methods in statistics, e.g. least squares; lots of examples; minimal abstraction.
Table of Contents
Preface; Reading guide; 1. Introduction; 2. Notations 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 semi-parametric models; 12. M-estimators; Appendix; References; Author index; Subject index; List of symbols.