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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, China

    Yi Wu, Xue-jun Wang & Shu-he Hu

Authors
  1. Yi Wu
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  2. Xue-jun Wang
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  3. Shu-he Hu
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Corresponding author

Correspondence to Xue-jun Wang.

Additional information

Supported by the National Natural Science Foundation of China (11501004, 11501005, 11526033, 11671012), the Natural Science Foundation of Anhui Province (1508085J06, 1608085QA02), the Key Projects for Academic Talent of Anhui Province (gxbjZD2016005) and the Research Teaching Model Curriculum of Anhui University (xjyjkc1407).

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Wu, Y., Wang, Xj. & Hu, Sh. Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications. Appl. Math. J. Chin. Univ. 31, 439–457 (2016). https://doi.org/10.1007/s11766-016-3406-z

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