Description
Book SynopsisThe theory of empirical processes provides valuable tools for the development of asymptotic theory in (nonparametric) statistical models, and makes possible 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. Graduate students and professionals in statistics as well as those with an interest in applications, to such area
Trade Review'… 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
Table of ContentsPreface; 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.
