Introduction to Nonparametric Estimation

Nonparametric estimators.- Lower bounds on the minimax risk.- Asymptotic efficiency and adaptation.

From the reviews:

"The book is meant to be an introduction to the rich theory of nonparametric estimation through some simple models and examples. The detailed proofs given in the book will help the interested reader to understand the subject better. This well written book will be welcomed by all those interested in learning the presented concepts. The author should be complimented for a good treatise with detailed proofs of several important results in nonparametric estimation theory." (Ravi Sreenivasan, Zentralblatt MATH, Vol. 1176, 2010)

"...A short and rigorous introduction to minimax results for estimators of densities and regression functions from independent observations. Each of the three chapters ends with a section containing detailed biographical notes and a section with exercises complementing and illustrating the main results. This book is an excellent introduction to the results and techniques of minimax estimation." (Journal of the American Statistical Association, Vol. 105, No. 489)

"The potential reader of this book should be conversant with functional analysis and topology ... . for a broad spectrum of mathematical statisticians, especially in the Continental Europe, this will be welcome as a good reading material. ... attempts to formulate the basic theory of nonparametric functional estimation, including (i) construction of such estimators, (ii) their (asymptotic) statistical properties, (iii) optimality, in some sense, and (iv) adaptive estimation. The author contends to present the material ... in a broad sense more acceptable to statisticians." (Pranab K. Sen, International Statistical Review, Vol. 79 (2), 2011)

From the reviews:

"The book is meant to be an introduction to the rich theory of nonparametric estimation through some simple models and examples. The detailed proofs given in the book will help the interested reader to understand the subject better. This well written book will be welcomed by all those interested in learning the presented concepts. The author should be complimented for a good treatise with detailed proofs of several important results in nonparametric estimation theory." (Ravi Sreenivasan, Zentralblatt MATH, Vol. 1176, 2010)

"...A short and rigorous introduction to minimax results for estimators of densities and regression functions from independent observations. Each of the three chapters ends with a section containing detailed biographical notes and a section with exercises complementing and illustrating the main results. This book is an excellent introduction to the results and techniques of minimax estimation." (Journal of the American Statistical Association, Vol. 105, No. 489)

"The potential reader of this book should be conversant with functional analysis and topology ... . for a broad spectrum of mathematical statisticians, especially in the Continental Europe, this will be welcome as a good reading material. ... attempts to formulate the basic theory of nonparametric functional estimation, including (i) construction of such estimators, (ii) their (asymptotic) statistical properties, (iii) optimality, in some sense, and (iv) adaptive estimation. The author contends to present the material ... in a broad sense more acceptable to statisticians." (Pranab K. Sen, International Statistical Review, Vol. 79 (2), 2011)