Strong Approximations in Probability and Statistics
eBook - PDF

Strong Approximations in Probability and Statistics

  1. 286 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Strong Approximations in Probability and Statistics

About this book

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.

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Yes, you can access Strong Approximations in Probability and Statistics by M. Csörgo,P. Révész, Z. W. Birnbaum,E. Lukacs in PDF and/or ePUB format, as well as other popular books in Mathematics & Applied Mathematics. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Academic Press
Year
2014
Print ISBN
9780121985400
eBook ISBN
9781483268040
Topic
Mathematics
Subtopic
Applied Mathematics
Index
Mathematics

Table of contents

  1. Front Cover
  2. Strong Approximations in Probability and Statistics
  3. Copyright Page
  4. Table of Contents
  5. Preface
  6. Introduction
  7. Chapter 1. Wiener and some Related Gaussian Processes
  8. Chapter 2. Strong Approximations of Partial Sums of I. I.D.R.V. by Wiener Processes
  9. Chapter 3. A Study of Partial Sums with the Help of Strong Approximation Methods
  10. Chapter 4. Strong Approximations of Empirical Processes by Gaussian Processes
  11. Chapter 5. A Study of Empirical and Quantile Processes with the Help of Strong Approximation Methods
  12. Chapter 6. A Study of Further Empirical Processes with the Help of Strong Approximation Methods
  13. Chapter 7. Random Limit Theorems via Strong Invariance Principles
  14. References
  15. Author Index
  16. Subject Index
  17. Summary of Notations and Abbreviations