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Weighted sums of strongly mixing random variables with an application to nonparametric regression

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  • Thanh, Le Van
  • Yin, G.

Abstract

This note establishes complete convergence for weighted sums of strongly mixing random variables. The result obtained is sharp. If the condition is relaxed slightly, the desired complete convergence does not hold, which is illustrated by two examples. An application of the main result to nonparametric regression is also considered.

Suggested Citation

  • Thanh, Le Van & Yin, G., 2015. "Weighted sums of strongly mixing random variables with an application to nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 195-202.
    • Handle: RePEc:eee:stapro:v:105:y:2015:i:c:p:195-202
    DOI: 10.1016/j.spl.2015.05.022
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    References listed on IDEAS

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    1. Aiting Shen & Xinghui Wang & Xiaoqin Li & Xuejun Wang, 2014. "On the Rate of Complete Convergence for Weighted Sums of Arrays of Rowwise ϕ-Mixing Random Variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(13), pages 2714-2725, July.
    2. 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.
    3. Georgiev, Alexander A., 1988. "Consistent nonparametric multiple regression: The fixed design case," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 100-110, April.
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    Cited by:

    1. Yi Wu & Xuejun Wang & Aiting Shen, 2023. "Strong Convergence for Weighted Sums of Widely Orthant Dependent Random Variables and Applications," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-28, March.

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