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Complete moment convergence for weighted sums of weakly dependent random variables and its application in nonparametric regression model

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  • Wu, Yi
  • Wang, Xuejun
  • Hu, Shuhe

Abstract

In this paper, some results on the complete moment convergence for weighted sums of weakly dependent (or ρ∗-mixing) random variables are established. The results obtained in this paper improve and extend the corresponding one of Sung (2010). As an application of the main results, we present a result on complete consistency for the weighted estimator in a nonparametric regression model based on ρ∗-mixing errors.

Suggested Citation

  • Wu, Yi & Wang, Xuejun & Hu, Shuhe, 2017. "Complete moment convergence for weighted sums of weakly dependent random variables and its application in nonparametric regression model," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 56-66.
    • Handle: RePEc:eee:stapro:v:127:y:2017:i:c:p:56-66
    DOI: 10.1016/j.spl.2017.03.027
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    References listed on IDEAS

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    1. Fan, Y., 1990. "Consistent nonparametric multiple regression for dependent heterogeneous processes: The fixed design case," Journal of Multivariate Analysis, Elsevier, vol. 33(1), pages 72-88, April.
    2. Roussas, George G., 1989. "Consistent regression estimation with fixed design points under dependence conditions," Statistics & Probability Letters, Elsevier, vol. 8(1), pages 41-50, May.
    3. Liang, Han-Ying & Jing, Bing-Yi, 2005. "Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 227-245, August.
    4. Guo, Mingle & Zhu, Dongjin, 2013. "Equivalent conditions of complete moment convergence of weighted sums for ρ∗-mixing sequence of random variables," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 13-20.
    5. Roussas, George G. & Tran, Lanh T. & Ioannides, D. A., 1992. "Fixed design regression for time series: Asymptotic normality," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 262-291, February.
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    Cited by:

    1. Yi Wu & Xuejun Wang & Aiting Shen, 2021. "Strong convergence properties for weighted sums of m-asymptotic negatively associated random variables and statistical applications," Statistical Papers, Springer, vol. 62(5), pages 2169-2194, October.

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