Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications |
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Authors: | Xuejun Wang Xin Deng Lulu Zheng Shuhe Hu |
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Affiliation: | 1. School of Mathematical Science, Anhui University, Hefei 230601, People's Republic of China07019@ahu.edu.cn;3. School of Mathematical Science, Anhui University, Hefei 230601, People's Republic of China |
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Abstract: | In this paper, the Rosenthal-type maximal inequalities and Kolmogorov-type exponential inequality for negatively superadditive-dependent (NSD) random variables are presented. By using these inequalities, we study the complete convergence for arrays of rowwise NSD random variables. As applications, the Baum–Katz-type result for arrays of rowwise NSD random variables and the complete consistency for the estimator of nonparametric regression model based on NSD errors are obtained. Our results extend and improve the corresponding ones of Chen et al. [On complete convergence for arrays of rowwise negatively associated random variables. Theory Probab Appl. 2007;52(2):393–397] for arrays of rowwise negatively associated random variables to the case of arrays of rowwise NSD random variables. |
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Keywords: | Rosenthal-type maximal inequality Kolmogorov-type exponential inequality negatively superadditive-dependent random variables complete convergence complete consistency |
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