Conditional limit theorems for conditionally negatively associated random variables |
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Authors: | De-Mei Yuan Jun An Xiu-Shan Wu |
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Institution: | 1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China
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Abstract: | From the ordinary notion of negative association for a sequence of random variables, a new concept called conditional negative
association is introduced. The relation between negative association and conditional negative association is answered, that
is, the negative association does not imply the conditional negative association, and vice versa. The basic properties of
conditional negative association are developed, which extend the corresponding ones under the non-conditioning setup. By means
of these properties, some Rosenthal type inequalities for maximum partial sums of such sequences of random variables are derived,
which extend the corresponding results for negatively associated random variables. As applications of these inequalities,
some conditional mean convergence theorems, conditionally complete convergence results and a conditional central limit theorem
stated in terms of conditional characteristic functions are established. In addition, some lemmas in the context are of independent
interest. |
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Keywords: | |
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