[PDF] Notes On Empirical Processes eBook

Author : Michael R. Kosorok
Publisher : Springer Science & Business Media
Page : 482 pages
File Size : 48,36 MB
Release : 2007-12-29
Category : Mathematics
ISBN : 0387749780

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Kosorok’s brilliant text provides a self-contained introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. This is an authoritative text that covers all the bases, and also a friendly and gradual introduction to the area. The book can be used as research reference and textbook.

Author : Galen R. Shorack
Publisher : SIAM
Page : 992 pages
File Size : 40,5 MB
Release : 2009-01-01
Category : Mathematics
ISBN : 0898719011

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Originally published in 1986, this valuable reference provides a detailed treatment of limit theorems and inequalities for empirical processes of real-valued random variables; applications of the theory to censored data, spacings, rank statistics, quantiles, and many functionals of empirical processes, including a treatment of bootstrap methods; and a summary of inequalities that are useful for proving limit theorems. At the end of the Errata section, the authors have supplied references to solutions for 11 of the 19 Open Questions provided in the book's original edition. Audience: researchers in statistical theory, probability theory, biostatistics, econometrics, and computer science.

Author : Hira L. Koul
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 47,76 MB
Release : 2002-06-13
Category : Mathematics
ISBN : 9780387954769

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This book presents a unified approach for obtaining the limiting distributions of minimum distance. It discusses classes of goodness-of-t tests for fitting an error distribution in some of these models and/or fitting a regression-autoregressive function without assuming the knowledge of the error distribution. The main tool is the asymptotic equi-continuity of certain basic weighted residual empirical processes in the uniform and L2 metrics.

Author : Vladimir Koltchinskii
Publisher : Springer
Page : 259 pages
File Size : 38,97 MB
Release : 2011-07-29
Category : Mathematics
ISBN : 3642221475

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The purpose of these lecture notes is to provide an introduction to the general theory of empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities in penalized problems. In recent years, there have been new developments in this area motivated by the study of new classes of methods in machine learning such as large margin classification methods (boosting, kernel machines). The main probabilistic tools involved in the analysis of these problems are concentration and deviation inequalities by Talagrand along with other methods of empirical processes theory (symmetrization inequalities, contraction inequality for Rademacher sums, entropy and generic chaining bounds). Sparse recovery based on l_1-type penalization and low rank matrix recovery based on the nuclear norm penalization are other active areas of research, where the main problems can be stated in the framework of penalized empirical risk minimization, and concentration inequalities and empirical processes tools have proved to be very useful.

Author : D. Pollard
Publisher : David Pollard
Page : 223 pages
File Size : 20,12 MB
Release : 1984-10-08
Category : Mathematics
ISBN : 0387909907

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Functionals on stochastic processes; Uniform convergence of empirical measures; Convergence in distribution in euclidean spaces; Convergence in distribution in metric spaces; The uniform metric on space of cadlag functions; The skorohod metric on D [0, oo); Central limit teorems; Martingales.

Author : Roman Vershynin
Publisher : Cambridge University Press
Page : 299 pages
File Size : 15,21 MB
Release : 2018-09-27
Category : Business & Economics
ISBN : 1108415199

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An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Author : Art B. Owen
Publisher : CRC Press
Page : 322 pages
File Size : 28,40 MB
Release : 2001-05-18
Category : Mathematics
ISBN : 1420036157

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Empirical likelihood provides inferences whose validity does not depend on specifying a parametric model for the data. Because it uses a likelihood, the method has certain inherent advantages over resampling methods: it uses the data to determine the shape of the confidence regions, and it makes it easy to combined data from multiple sources. It al