Convergence Rates for Weighted Sums of Random Variables

摘要

Let X sub 1, X sub 2, ... be independent random variables and let a sub (nk) be constants. Let S sub n = 1/n (Summation from k=1 to k=n of (X sub k - EX sub k)) and let A sub n = Summation from k=1 to k = infinity, of a sub (nk) (X sub k - EX sub k). The main purpose of this study was the investigation of the rate of convergence of P(absolute value of A sub n > epsilon) to zero under various assumptions on the X sub k's. In addition to the main results, results were obtained in ergodic theory, maximum likelihood estimation, testing against trend, and bidding theory. (Author)