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 elegantproofs. 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. This book will be useful for researchers and grad students interested in theoretical aspects of smoothing techniques. Many important and useful results on optimal and adaptive estimation are provided. Concise and self-contained treatment of the theory Thorough analysis of optimality and adaptivity issues Detailed account on minimax lower bounds INDICE: Nonparametric estimators.- Lower bounds on the minimax risk.- Asymptotic efficiency and adaptation.- Appendix.- References.- Index.
- ISBN: 978-0-387-79051-0
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 225
- Fecha Publicación: 01/02/2009
- Nº Volúmenes: 1
- Idioma: Inglés