Lp-Approximable Sequences of Vectors and Limit Distribution of Quadratic Forms of Random Variables
Author: Mynbaev K.T.
Source: Advances in Applied Mathematics, Volume 26, Number 4, May 2001 , pp. 302-329(28)
Publisher: Academic Press
The properties of L2-approximable sequences established here form a complete toolkit for statistical results concerning weighted sums of random variables, where the weights are nonstochastic sequences approximated in some sense by square-integrable functions and the random variables are two-wing averages of martingale differences. The results constitute the first significant advancement in the theory of L2-approximable sequences since 1976 when Moussatat introduced a narrower notion of L2-generated sequences. The method relies on a study of certain linear operators in the spaces Lp and lp. A criterion of Lp-approximability is given. The results are new even when the weight generating function is identically 1. A central limit theorem for quadratic forms of random variables illustrates the method. Copyright 2001 Academic Press.
Document Type: Research article
Affiliations: Kazakhstan Institute of Management, Economics, and Strategic Research, 4, Abai Avenue, Room 207, Almaty, 480100, Kazakhstan
Publication date: 2001-05-01