Central Limit Theorems for Empirical Processes Based on Stochastic Processes
Title | Central Limit Theorems for Empirical Processes Based on Stochastic Processes PDF eBook |
Author | Yuping Yang |
Publisher | |
Pages | |
Release | 2013 |
Genre | |
ISBN |
Empirical Processes
Title | Empirical Processes PDF eBook |
Author | David Pollard |
Publisher | IMS |
Pages | 100 |
Release | 1990 |
Genre | Distribution (Probability theory). |
ISBN | 9780940600164 |
Empirical Processes
Title | Empirical Processes PDF eBook |
Author | Peter Gänssler |
Publisher | IMS |
Pages | 200 |
Release | 1983 |
Genre | Philosophy |
ISBN | 9780940600034 |
Uniform Central Limit Theorems
Title | Uniform Central Limit Theorems PDF eBook |
Author | R. M. Dudley |
Publisher | Cambridge University Press |
Pages | 485 |
Release | 2014-02-24 |
Genre | Mathematics |
ISBN | 1107728886 |
In this new edition of a classic work on empirical processes the author, an acknowledged expert, gives a thorough treatment of the subject with the addition of several proved theorems not included in the first edition, including the Bretagnolle–Massart theorem giving constants in the Komlos–Major–Tusnady rate of convergence for the classical empirical process, Massart's form of the Dvoretzky–Kiefer–Wolfowitz inequality with precise constant, Talagrand's generic chaining approach to boundedness of Gaussian processes, a characterization of uniform Glivenko–Cantelli classes of functions, Giné and Zinn's characterization of uniform Donsker classes, and the Bousquet–Koltchinskii–Panchenko theorem that the convex hull of a uniform Donsker class is uniform Donsker. The book will be an essential reference for mathematicians working in infinite-dimensional central limit theorems, mathematical statisticians, and computer scientists working in computer learning theory. Problems are included at the end of each chapter so the book can also be used as an advanced text.
Limit Theorems for Randomly Stopped Stochastic Processes
Title | Limit Theorems for Randomly Stopped Stochastic Processes PDF eBook |
Author | Dmitrii S. Silvestrov |
Publisher | Springer Science & Business Media |
Pages | 408 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 0857293907 |
This volume is the first to present a state-of-the-art overview of this field, with many results published for the first time. It covers the general conditions as well as the basic applications of the theory, and it covers and demystifies the vast and technically demanding Russian literature in detail. Its coverage is thorough, streamlined and arranged according to difficulty.
Convergence of Stochastic Processes
Title | Convergence of Stochastic Processes PDF eBook |
Author | D. Pollard |
Publisher | Springer Science & Business Media |
Pages | 228 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461252547 |
A more accurate title for this book might be: An Exposition of Selected Parts of Empirical Process Theory, With Related Interesting Facts About Weak Convergence, and Applications to Mathematical Statistics. The high points are Chapters II and VII, which describe some of the developments inspired by Richard Dudley's 1978 paper. There I explain the combinatorial ideas and approximation methods that are needed to prove maximal inequalities for empirical processes indexed by classes of sets or classes of functions. The material is somewhat arbitrarily divided into results used to prove consistency theorems and results used to prove central limit theorems. This has allowed me to put the easier material in Chapter II, with the hope of enticing the casual reader to delve deeper. Chapters III through VI deal with more classical material, as seen from a different perspective. The novelties are: convergence for measures that don't live on borel a-fields; the joys of working with the uniform metric on D[O, IJ; and finite-dimensional approximation as the unifying idea behind weak convergence. Uniform tightness reappears in disguise as a condition that justifies the finite-dimensional approximation. Only later is it exploited as a method for proving the existence of limit distributions. The last chapter has a heuristic flavor. I didn't want to confuse the martingale issues with the martingale facts.
Introduction to Empirical Processes and Semiparametric Inference
Title | Introduction to Empirical Processes and Semiparametric Inference PDF eBook |
Author | Michael R. Kosorok |
Publisher | Springer Science & Business Media |
Pages | 482 |
Release | 2007-12-29 |
Genre | Mathematics |
ISBN | 0387749780 |
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.