Reproducing kernel Hilbert spaces in probability and statistics. With a preface by Persi Diaconis. (English) Zbl 1145.62002

Berlinet, Alain; Thomas-Agnan, Christine

Boston, MA: Kluwer Academic Publishers (ISBN 1-4020-7679-7/hbk). xxii, 355 p. (2004).

From the introduction: The theory of reproducing kernel Hilbert spaces interacts with many subjects in mathematics. In this book we present the main points of this theory and study examples of its use in probability and mathematical statistics. The aim is to provide mathematical tools for handling problems arising in these areas with the intention of putting together topics apparently different but sharing the same background. These include statistical signal processing, nonparametric curve estimation, random measures and limit theorems. Through the applications of reproducing kernels, the book is intended to present an accurate picture of some developments in probability and mathematical statistics, without any attempt at an exhaustive description. The text is geared to graduate students in statistics, mathematics or engineering, or to scientists at an equivalent level.

MSC:

62-02	Research exposition (monographs, survey articles) pertaining to statistics
46E22	Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
46N30	Applications of functional analysis in probability theory and statistics
60G35	Signal detection and filtering (aspects of stochastic processes)
60G57	Random measures
62G05	Nonparametric estimation
62M20	Inference from stochastic processes and prediction
94A12	Signal theory (characterization, reconstruction, filtering, etc.)

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