TY  - BOOK
AU  - Tsybakov,Alexandre B.
ED  - SpringerLink (Online service)
TI  - Introduction to Nonparametric Estimation
T2  - Springer Series in Statistics,
SN  - 9780387790527
AV  - QA276-280 
U1  - 519.5 23
PY  - 2009///
CY  - New York, NY
PB  - Springer New York
KW  - Mathematical statistics
KW  - Computer science
KW  - Optical pattern recognition
KW  - Econometrics
KW  - Distribution (Probability theory
KW  - Statistical Theory and Methods
KW  - Probability and Statistics in Computer Science
KW  - Pattern Recognition
KW  - Signal, Image and Speech Processing
KW  - Probability Theory and Stochastic Processes
N1  - Nonparametric estimators -- Lower bounds on the minimax risk -- Asymptotic efficiency and adaptation
N2  - Methods of nonparametric estimation are located at the core of modern statistical science. The aim of this book is to give a short but mathematically self-contained introduction to the theory of nonparametric estimation. The emphasis is on the construction of optimal estimators; therefore the concepts of minimax optimality and adaptivity, as well as the oracle approach, occupy the central place in the book. 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 elegant proofs. 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
UR  - https://doi.org/10.1007/b13794
ER  -