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Exponential probability inequality for \(m\)-END random variables and its applications

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Abstract

The concept of \(m\)-extended negatively dependent (\(m\)-END, in short) random variables is introduced and the Kolmogorov exponential inequality for \(m\)-END random variables is established. As applications of the Kolmogorov exponential inequality, we further investigate the complete convergence for arrays of rowwise \(m\)-END random variables and the complete consistency for the estimator of nonparametric regression models based on \(m\)-END errors. Our results generalize and improve some known ones for independent random variables and dependent random variables.

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Acknowledgments

The authors are most grateful to the anonymous referees for careful reading of the manuscript and valuable suggestions which helped to improve an earlier version of this paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, People’s Republic of China

    Xuejun Wang, Yi Wu & Shuhe Hu

Authors
  1. Xuejun Wang
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  2. Yi Wu
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  3. Shuhe Hu
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Corresponding author

Correspondence to Xuejun Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (11201001, 11171001, 11426032), the National Social Science Foundation of China (14ATJ005), the Natural Science Foundation of Anhui Province (1508085J06) and the Research Teaching Model Curriculum of Anhui University (xjyjkc1407).

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Wang, X., Wu, Y. & Hu, S. Exponential probability inequality for \(m\)-END random variables and its applications. Metrika 79, 127–147 (2016). https://doi.org/10.1007/s00184-015-0547-7

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  • DOI: https://doi.org/10.1007/s00184-015-0547-7

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