تقریب‌های قوی در احتمال و آمار (تقریب ۲۸۴ صفحه) (احتمال و آمار ریاضی، جلد ۴۲) (مونوگرافی احتمال و آمار ریاضی)

Strong Approximations in Probability and Statistics presents strong invariance type results for partial sums and empirical processes of independent and identically distributed random variables (IIDRV). This seven-chapter text emphasizes the applicability of strong approximation methodology to a variety of problems of probability and statistics. Chapter 1 evaluates the theorems for Wiener and Gaussian processes that can be extended to partial sums and empirical processes of IIDRV through strong approximation methods, while Chapter 2 addresses the problem of best possible strong approximations of partial sums of IIDRV by a Wiener process. Chapters 3 and 4 contain theorems concerning the one-time parameter Wiener process and strong approximation for the empirical and quantile processes based on IIDRV. Chapter 5 demonstrate the validity of previously discussed theorems, including Brownian bridges and Kiefer process, for empirical and quantile processes. Chapter 6 illustrate the approximation of defined sequences of empirical density, regression, and characteristic functions by appropriate Gaussian processes. Chapter 7 deal with the application of strong approximation methodology to study weak and strong convergence properties of random size partial sum and empirical processes. This book will prove useful to mathematicians and advance mathematics students. Content: Front Matter, Page 3 Copyright, Page 4 Preface, Pages 9-10 Introduction, Pages 11-19 1 - Wiener and some Related Gaussian Processes, Pages 21-87 2 - Strong Approximations of Partial Sums of I.I.D.R.V. by Wiener Processes, Pages 88-114 3 - A Study of Partial Sums with the Help of Strong Approximation Methods, Pages 115-126 4 - Strong Approximations of Empirical Processes by Gaussian Processes, Pages 127-155 5 - A Study of Empirical and Quantile Processes with the Help of Strong Approximation Methods, Pages 156-218 6 - A Study of Further Empirical Processes with the Help of Strong Approximation Methods, Pages 219-249 7 - Random Limit Theorems via Strong Invariance Principles, Pages 250-262 References, Pages 263-275 Author Index, Pages 277-279 Subject Index, Pages 281-282 Summary of Notations and Abbrevations, Pages 283-284 Probability and Mathematical Statistics: A Series of Monographs and Textbooks, Pages ibc1-ibc2 M. Csörgö And P. Révész. Includes Indexes. Bibliography: P. [263]-275.