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Some convergence properties for partial sums of widely orthant dependent random variables and their statistical applications

Author

Listed:
  • Mengmei Xi

    (Anhui University)

  • Rui Wang

    (Anhui University)

  • Zhaoyang Cheng

    (Wendian College, Anhui University)

  • Xuejun Wang

    (Anhui University)

Abstract

In this paper, we present the $$L_p$$ L p convergence for partial sums $$S_n=\sum _{k=1}^nX_k$$ S n = ∑ k = 1 n X k under the Cesàro uniform integrability condition and the complete convergence for the maximum of $$S_n$$ S n for sequences of widely orthant dependent random variables $$\{X_n,n\ge 1\}.$$ { X n , n ≥ 1 } . Some of the results extend the corresponding ones in reference. As applications, we get the complete consistency and the strong consistency for the estimator in a nonparametric regression model.

Suggested Citation

  • Mengmei Xi & Rui Wang & Zhaoyang Cheng & Xuejun Wang, 2020. "Some convergence properties for partial sums of widely orthant dependent random variables and their statistical applications," Statistical Papers, Springer, vol. 61(4), pages 1663-1684, August.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:4:d:10.1007_s00362-018-0996-y
    DOI: 10.1007/s00362-018-0996-y
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    References listed on IDEAS

    as
    1. Aiting Shen, 2013. "Bernstein-Type Inequality for Widely Dependent Sequence and Its Application to Nonparametric Regression Models," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, July.
    2. Xuejun Wang & Chen Xu & Tien-Chung Hu & Andrei Volodin & Shuhe Hu, 2014. "On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 607-629, September.
    3. 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.
    4. 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.
    5. Kaiyong Wang & Yuebao Wang & Qingwu Gao, 2013. "Uniform Asymptotics for the Finite-Time Ruin Probability of a Dependent Risk Model with a Constant Interest Rate," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 109-124, March.
    6. Liu, Li, 2009. "Precise large deviations for dependent random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1290-1298, May.
    7. Xuejun Wang & Zeyu Si, 2015. "Complete consistency of the estimator of nonparametric regression model under ND sequence," Statistical Papers, Springer, vol. 56(3), pages 585-596, August.
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