Mynbaev, Kairat (2000): $L_p$Approximable sequences of vectors and limit distribution of quadratic forms of random variables. Published in: Advances in Applied Mathematics , Vol. 26, (2001): pp. 302329.

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Abstract
The properties of $L_2$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 squareintegrable functions and the random variables are "twowing" averages of martingale differences. The results constitute the first significant advancement in the theory of $L_2$approximable sequences since 1976 when Moussatat introduced a narrower notion of $L_2$generated sequences. The method relies on a study of certain linear operators in the spaces $L_p$ and $l_p$. A criterion of $L_p$approximability is given. The results are new even when the weights generating function is identically 1. A central limit theorem for quadratic forms of random variables illustrates the method.
Item Type:  MPRA Paper 

Original Title:  $L_p$Approximable sequences of vectors and limit distribution of quadratic forms of random variables 
Language:  English 
Keywords:  linear operators in $L_p$ spaces; central limit theorem; quadratic forms of random variables 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  18447 
Depositing User:  Kairat Mynbaev 
Date Deposited:  08. Nov 2009 06:36 
Last Modified:  12. Feb 2013 02:49 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/18447 