Mathematical Foundations of Infinite-Dimensional Statistical Models

Evarist Giné

ISBN 10: 1107043166 / ISBN 13: 9781107043169

Verlag: Cambridge University Press, 2015

Beschreibung

Druck auf Anfrage Neuware - Printed after ordering - In nonparametric and high-dimensional statistical models, the classical Gauss-Fisher-Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, on approximation and wavelet theory, and on the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is then presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In the final chapter, the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions.

Bestandsnummer des Verkäufers 9781107043169

Bibliografische Details

• Titel: Mathematical Foundations of Infinite-Dimensional Statistical Models
• Verlag: Cambridge University Press
• Erscheinungsjahr: 2015
• Sprache: Englisch
• ISBN-10: 1107043166
• ISBN-13: 9781107043169
• Einband: Buch
• Zustand: Neu
• Abmessungen: 260B x 183 H x 42 T Millimeter Breite: 260 mm, Höhe: 183 mm, Tiefe: 42 mm
• Gewicht: 1500 Gramm

Über diesen Titel

Inhaltsangabe

In nonparametric and high-dimensional statistical models, the classical Gauss-Fisher-Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, on approximation and wavelet theory, and on the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is then presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In the final chapter, the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions.

Über die Autorinnen und Autoren

Evarist Giné (1944–2015) was Head of the Department of Mathematics at the University of Connecticut. Giné was a distinguished mathematician who worked on mathematical statistics and probability in infinite dimensions. He was the author of two books and more than 100 articles.

Richard Nickl is a Reader in Mathematical Statistics in the Statistical Laboratory within the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge.