Relative Weak Compactness of Sums of Random Variables
- Authors: Golikova N.N.1, Kruglov V.M.2
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Affiliations:
- Faculty of Physics and Mathematics
- Department of Statistics, Faculty of Computational Mathematics and Cybernetics
- Issue: Vol 39, No 3 (2018)
- Pages: 331-339
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/201787
- DOI: https://doi.org/10.1134/S1995080218030137
- ID: 201787
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Abstract
In this article sufficient conditions for relative weak compactness of sums centered by constants of pair-wise negatively associated randomvariables and for sums of squares of any random variables centered by their medians are given. These conditions become necessary and sufficient if random variables are independent. The conditions are inspired by classical conditions for weak convergence of sums of uniformly small random variables.
About the authors
N. N. Golikova
Faculty of Physics and Mathematics
Author for correspondence.
Email: nina.golikova@mail.ru
Russian Federation, ul. Radio 10a, Moscow, 105005
V. M. Kruglov
Department of Statistics, Faculty of Computational Mathematics and Cybernetics
Email: nina.golikova@mail.ru
Russian Federation, Moscow, 119992