首页 | 本学科首页   官方微博 | 高级检索  
     


Lp-Approximable Sequences of Vectors and Limit Distribution of Quadratic Forms of Random Variables
Authors:Kairat T. Mynbaev
Affiliation:Kazakhstan Institute of Management, Economics, and Strategic Research, 4, Abai Avenue, Room 207, 480100, Almaty, Kazakhstanf1
Abstract: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.
Keywords:linear operators in Lp spaces   central limit theorem   quadratic forms of random variables
本文献已被 ScienceDirect 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号