On the Kolmogorov inequalities for quadratic forms of dependent uniformly bounded random variables

Some Kolmogorov probability inequalities for quadratic forms and weighted quadratic forms of negative superadditive dependent (NSD) uniformly bounded random variables are provided. Using these inequalities, some complete convergence of randomized quadratic forms under some suitable conditions are ev...

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Bibliographic Details
Published in:Statistics & probability letters 2011-08, Vol.81 (8), p.1112-1120
Main Authors: Eghbal, N., Amini, M., Bozorgnia, A.
Format: Article
Language:English
Subjects:
Complete convergence
Exact sciences and technology
General topics
Kolmogorov inequality
Kolmogorov inequality Negative superadditive dependent Quadratic forms Complete convergence
Mathematics
Negative superadditive dependent
Probability and statistics
Probability theory and stochastic processes
Quadratic forms
Sciences and techniques of general use
Statistics
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Summary:Some Kolmogorov probability inequalities for quadratic forms and weighted quadratic forms of negative superadditive dependent (NSD) uniformly bounded random variables are provided. Using these inequalities, some complete convergence of randomized quadratic forms under some suitable conditions are evaluated. Moreover, various examples are presented in which the given conditions of our results are satisfied.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2011.03.005