Author : R. M. Dudley
Publisher : Cambridge University Press
Page : 485 pages
File Size : 16,94 MB
Release : 2014-02-24
Category : Mathematics
ISBN : 0521498848
This expanded edition of the classic work on empirical processes now boasts several new proved theorems not in the first.
Author : Ernst Eberlein
Publisher : Birkhäuser
Page : 336 pages
File Size : 42,15 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3034888295
What is high dimensional probability? Under this broad name we collect topics with a common philosophy, where the idea of high dimension plays a key role, either in the problem or in the methods by which it is approached. Let us give a specific example that can be immediately understood, that of Gaussian processes. Roughly speaking, before 1970, the Gaussian processes that were studied were indexed by a subset of Euclidean space, mostly with dimension at most three. Assuming some regularity on the covariance, one tried to take advantage of the structure of the index set. Around 1970 it was understood, in particular by Dudley, Feldman, Gross, and Segal that a more abstract and intrinsic point of view was much more fruitful. The index set was no longer considered as a subset of Euclidean space, but simply as a metric space with the metric canonically induced by the process. This shift in perspective subsequently lead to a considerable clarification of many aspects of Gaussian process theory, and also to its applications in other settings.
Author : Evarist Giné
Publisher : Springer
Page : 431 pages
File Size : 10,79 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 354069210X
Nur Contents aufnehmen
Author : B. Grigelionis
Publisher : Walter de Gruyter GmbH & Co KG
Page : 752 pages
File Size : 43,25 MB
Release : 2020-05-18
Category : Mathematics
ISBN : 311231932X
No detailed description available for "Probability Theory and Mathematical Statistics".
Author : Taĭvo Viktorovich Arak
Publisher : American Mathematical Soc.
Page : 236 pages
File Size : 35,17 MB
Release : 1988
Category : Mathematics
ISBN : 9780821831182
Among the diverse constructions studied in modern probability theory, the scheme for summation of independent random variables occupies a special place. This book presents a study of distributions of sums of independent random variables with minimal restrictions imposed on their distributions.
Author : Evarist Giné
Publisher : Cambridge University Press
Page : 706 pages
File Size : 44,10 MB
Release : 2021-03-25
Category : Mathematics
ISBN : 1009022784
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, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is 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 a 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. Winner of the 2017 PROSE Award for Mathematics.
Author : R. M. Dudley
Publisher : Cambridge University Press
Page : 452 pages
File Size : 37,61 MB
Release : 1999-07-28
Category : Mathematics
ISBN : 0521461022
This treatise by an acknowledged expert includes several topics not found in any previous book.
Author : P. Hall
Publisher : Academic Press
Page : 321 pages
File Size : 44,18 MB
Release : 2014-07-10
Category : Mathematics
ISBN : 1483263223
Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.
Author : Institute of Mathematical Statistics
Publisher :
Page : 730 pages
File Size : 25,40 MB
Release : 1996
Category : Mathematical statistics
ISBN :
Author : Alexandr A. Borovkov
Publisher : Springer Science & Business Media
Page : 742 pages
File Size : 40,96 MB
Release : 2013-06-22
Category : Mathematics
ISBN : 1447152018
This self-contained, comprehensive book tackles the principal problems and advanced questions of probability theory and random processes in 22 chapters, presented in a logical order but also suitable for dipping into. They include both classical and more recent results, such as large deviations theory, factorization identities, information theory, stochastic recursive sequences. The book is further distinguished by the inclusion of clear and illustrative proofs of the fundamental results that comprise many methodological improvements aimed at simplifying the arguments and making them more transparent. The importance of the Russian school in the development of probability theory has long been recognized. This book is the translation of the fifth edition of the highly successful Russian textbook. This edition includes a number of new sections, such as a new chapter on large deviation theory for random walks, which are of both theoretical and applied interest. The frequent references to Russian literature throughout this work lend a fresh dimension and make it an invaluable source of reference for Western researchers and advanced students in probability related subjects. Probability Theory will be of interest to both advanced undergraduate and graduate students studying probability theory and its applications. It can serve as a basis for several one-semester courses on probability theory and random processes as well as self-study.
