Bücher und Buch-Herausgaben:

M. Csörgő, P. Révész (Hrg.):
"Strong Approximations in Probability and Statistics (eBook)";
Academic Press / Elsevier, 2014, ISBN: 9781483268040; 286 S.

Kurzfassung englisch:
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.

Elektronische Version der Publikation:

Erstellt aus der Publikationsdatenbank der Technischen Universitšt Wien.