Ebook: Nonparametric Goodness-of-Fit Testing Under Gaussian Models

From the reviews:

"The book is self-contained, and the bibliography is very rich and in fact provides a comprehensive listing of references about minimax testing (something that heretofore had been missing from the field.) To get the best out of this book, the reader should be familiar with basic functional analysis, wavelet theory, and optimization for extreme problems…It is highly recommended to anyone who wants an introduction to hypothesis testing from the minimax approach–yet it is only a starting point, as Gaussian models are studied exclusively." Journal of the American Statistical Association, June 2004

"The book deals with nonparametric goodness-of-fit testing problems from the literature of the past twenty years. … It is a theoretical book with mathematical results … . The proofs of the theorems are very detailed and many details are in the appendix of more than one hundred pages." (N. D. C. Veraverbeke, Short Book Reviews, Vol. 24 (1), 2004)

"The present book is devoted to a modern theory of nonparametric goodness-of-fit testing. … The level of the book meets a quite high standard. The book will certainly be of interest to mathematical statisticians interested in the theory of nonparametric statistical interference, and also to specialists dealing with applied nonparametric statistical problems in signal detection and transmission, technical and medical diagnostics, and other fields." (Marie Huškova, Zentralblatt MATH, Vol. 1013, 2003)

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This book presents the modern theory of nonparametric goodness-of-fit testing. The study is based on an asymptotic version of the minimax approach. The methods for the construction of asymptotically optimal, rate optimal, and optimal adaptive test procedures are developed. The authors present many new results that demonstrate the principal differences between nonparametric goodness-of-fit testing problems with parametric goodness-of-fit testing problems and with non-parametric estimation problems. This book fills the gap in modern nonparametric statistical theory by discussing hypothesis testing.

The book is addressed to mathematical statisticians who are interesting in the theory of non-parametric statistical inference. It will be of interest to specialists who are dealing with applied non-parametric statistical problems that are relevant in signal detection and transmission and in technical and medical diagnostics among others.

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This book presents the modern theory of nonparametric goodness-of-fit testing. The study is based on an asymptotic version of the minimax approach. The methods for the construction of asymptotically optimal, rate optimal, and optimal adaptive test procedures are developed. The authors present many new results that demonstrate the principal differences between nonparametric goodness-of-fit testing problems with parametric goodness-of-fit testing problems and with non-parametric estimation problems. This book fills the gap in modern nonparametric statistical theory by discussing hypothesis testing.

The book is addressed to mathematical statisticians who are interesting in the theory of non-parametric statistical inference. It will be of interest to specialists who are dealing with applied non-parametric statistical problems that are relevant in signal detection and transmission and in technical and medical diagnostics among others.

Content:
Front Matter....Pages N2-xiv
Introduction....Pages 1-37
An Overview....Pages 38-80
Minimax Distinguishability....Pages 81-135
Sharp Asymptotics. I....Pages 136-184
Sharp Asymptotics. II....Pages 185-230
Gaussian Asymptotics for Power and Besov Norms....Pages 231-261
Adaptation for Power and Besov Norms....Pages 262-290
High-Dimensional Signal Detection....Pages 291-353
Back Matter....Pages 354-457

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This book presents the modern theory of nonparametric goodness-of-fit testing. The study is based on an asymptotic version of the minimax approach. The methods for the construction of asymptotically optimal, rate optimal, and optimal adaptive test procedures are developed. The authors present many new results that demonstrate the principal differences between nonparametric goodness-of-fit testing problems with parametric goodness-of-fit testing problems and with non-parametric estimation problems. This book fills the gap in modern nonparametric statistical theory by discussing hypothesis testing.

The book is addressed to mathematical statisticians who are interesting in the theory of non-parametric statistical inference. It will be of interest to specialists who are dealing with applied non-parametric statistical problems that are relevant in signal detection and transmission and in technical and medical diagnostics among others.

Content:
Front Matter....Pages N2-xiv
Introduction....Pages 1-37
An Overview....Pages 38-80
Minimax Distinguishability....Pages 81-135
Sharp Asymptotics. I....Pages 136-184
Sharp Asymptotics. II....Pages 185-230
Gaussian Asymptotics for Power and Besov Norms....Pages 231-261
Adaptation for Power and Besov Norms....Pages 262-290
High-Dimensional Signal Detection....Pages 291-353
Back Matter....Pages 354-457
....