Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications

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• 作者：Yi Wu ; Xue-jun Wang ; Shu-he Hu
• 关键词：exponential inequality ; complete convergence ; negatively superadditive ; dependent random variables ; nonparametric regression model ; complete consistency
• 刊名：Applied Mathematics-A Journal of Chinese Universities
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：31
• 期：4
• 页码：439-457
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Editorial Committee of Applied Mathematics - A Journal of Chinese Universities
• ISSN：1993-0445
• 卷排序：31

文摘

In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent (NSD, in short) random variables is established. By using the exponential inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28] and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors.