ON THE ASYMPTOTIC-BEHAVIOR OF THE MOVING BLOCK BOOTSTRAP FOR NORMALIZED SUMS OF HEAVY-TAIL RANDOM-VARIABLES

• 成果类型: Article
• 署名作者: LAHIRI, SN
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176324711
• 发表日期: 1995
• 页码: 1331-1349
• 关键词: mixing sequences; random vectors; sample-size; distributions; jackknife

摘要

This paper studies the performance of the moving block bootstrap procedure for normalized sums of dependent random variables. Suppose that X(1), X(2),... are stationary rho-mixing random variables with Sigma rho(2(i)) < infinity. Let T-n = (X(1) + ... + X(n) - b(n))/a(n), for some suitable constants a(n) and b(n), and let T-m,n(*), denote the moving block bootstrap version of T-n based on a bootstrap sample of size m. Under certain regularity conditions, it is shown that, for X(n)'s lying in the domain of partial attraction of certain infinitely divisible distributions, the conditional distribution (H) over cap(m,n) of T-m,n(*) provides a valid approximation to the distribution of T-n along every weakly convergent subsequence, provided m = o(n) as n --> infinity. On the other hand, for the usual choice of the resample size m = n, (H) over cap(n,n)(x) is shown to converge to a nondegenerate random limit as given by Athreya (1987) when T-n has a stable limit of order alpha, 1 < alpha < 2.