The theory of empirical processes provides valuable tools for the developmentof 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 parameterspace. Virtually all results are proved using only elementary ideas developedwithin 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 areas as econometrics, medical statistics, etc., will welcome this treatment. INDICE: 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 ofconvergence 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.
- ISBN: 978-0-521-12325-9
- Editorial: Cambridge University
- Encuadernacion: Rústica
- Páginas: 300
- Fecha Publicación: 28/01/2010
- Nº Volúmenes: 1
- Idioma: Inglés