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Exponential probability inequality for $$m$$ m -END random variables and its applications

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  • Xuejun Wang
  • Yi Wu
  • Shuhe Hu

Abstract

The concept of $$m$$ m -extended negatively dependent ( $$m$$ m -END, in short) random variables is introduced and the Kolmogorov exponential inequality for $$m$$ m -END random variables is established. As applications of the Kolmogorov exponential inequality, we further investigate the complete convergence for arrays of rowwise $$m$$ m -END random variables and the complete consistency for the estimator of nonparametric regression models based on $$m$$ m -END errors. Our results generalize and improve some known ones for independent random variables and dependent random variables. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • Xuejun Wang & Yi Wu & Shuhe Hu, 2016. "Exponential probability inequality for $$m$$ m -END random variables and its applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 127-147, February.
    • Handle: RePEc:spr:metrik:v:79:y:2016:i:2:p:127-147
    DOI: 10.1007/s00184-015-0547-7
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    References listed on IDEAS

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    1. Hongyan Fang & Saisai Ding & Xiaoqin Li & Wenzhi Yang, 2020. "Asymptotic Approximations of Ratio Moments Based on Dependent Sequences," Mathematics, MDPI, vol. 8(3), pages 1-18, March.

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