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An almost sure central limit theorem for self-normalized weighted sums

An almost sure central limit theorem for self-normalized weighted sums Let X,X 1 ,X 2, … be a sequence of nondegenerate i.i.d. random variables with zero means, which is in the domain of attraction of the normal law. Let {a ni ,1≤i≤n,n≥1} be an array of real numbers with some suitable conditions. In this paper, we show that a central limit theorem for self-normalized weighted sums holds. We also deduce a version of ASCLT for self-normalized weighted sums. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

An almost sure central limit theorem for self-normalized weighted sums

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Publisher
Springer Journals
Copyright
Copyright © 2013 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-010-8247-6
Publisher site
See Article on Publisher Site

Abstract

Let X,X 1 ,X 2, … be a sequence of nondegenerate i.i.d. random variables with zero means, which is in the domain of attraction of the normal law. Let {a ni ,1≤i≤n,n≥1} be an array of real numbers with some suitable conditions. In this paper, we show that a central limit theorem for self-normalized weighted sums holds. We also deduce a version of ASCLT for self-normalized weighted sums.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 20, 2013

References