Mathematical Foundations of Infinite-Dimensional Statistical Models - Couverture rigide

Livre 29 sur 45: Cambridge Series in Statistical and Probabilistic Mathematics

Giné, Evarist; Nickl, Richard

 
9781107043169: Mathematical Foundations of Infinite-Dimensional Statistical Models
Couverture rigide
ISBN 10 : 1107043166 ISBN 13 : 9781107043169
Editeur : Cambridge University Press, 2015

Synopsis

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.

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À propos des auteurs

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.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
2015
Langue
anglais
ISBN 10 
1107043166
ISBN 13 
9781107043169
Reliure
Relié
Nombre de pages
720
Coordonnées du fabricant
non disponible
Personne responsable
Avery
https://www.avery.fr/

chemin des peupliers 27
Dardilly
France

Autres éditions populaires du même titre

9781108994132: Mathematical Foundations of Infinite-Dimensional Statistical Models

Edition présentée

ISBN 10 :  110899413X ISBN 13 :  9781108994132
Editeur : Cambridge University Press, 2021
Couverture souple