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On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models

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  • Xuejun Wang
  • Chen Xu
  • Tien-Chung Hu
  • Andrei Volodin
  • Shuhe Hu

Abstract

In this paper, some probability inequalities and moment inequalities for widely orthant-dependent (WOD, in short) random variables are presented, especially the Marcinkiewicz–Zygmund type inequality and Rosenthal type inequality. By using these inequalities, we further study the complete convergence for weighted sums of arrays of row-wise WOD random variables and give some special cases, which extend some corresponding ones for dependent sequences. As applications, we present some sufficient conditions to prove the complete consistency for the estimator of nonparametric regression model based on WOD errors by using the complete convergence that we established. At last, the choice of the fixed design points and the weight functions for the nearest neighbor estimates is proposed. Our results generalize some known results for independent random variables and some dependent random variables. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:23:y:2014:i:3:p:607-629
    DOI: 10.1007/s11749-014-0365-7
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    1. Liang, Han-Ying, 2000. "Complete convergence for weighted sums of negatively associated random variables," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 317-325, July.
    2. 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.
    3. Christofides, Tasos C. & Vaggelatou, Eutichia, 2004. "A connection between supermodular ordering and positive/negative association," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 138-151, January.
    4. Liu, Xijun & Gao, Qingwu & Wang, Yuebao, 2012. "A note on a dependent risk model with constant interest rate," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 707-712.
    5. 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.
    6. Soo Sung, 2012. "Complete convergence for weighted sums of negatively dependent random variables," Statistical Papers, Springer, vol. 53(1), pages 73-82, February.
    7. 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.
    8. 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.
    9. 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.
    10. Kruglov, Victor M. & Volodin, Andrei I. & Hu, Tien-Chung, 2006. "On complete convergence for arrays," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1631-1640, September.
    11. Liu, Li, 2009. "Precise large deviations for dependent random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1290-1298, May.
    12. Sung, Soo Hak, 2007. "Complete convergence for weighted sums of random variables," Statistics & Probability Letters, Elsevier, vol. 77(3), pages 303-311, February.
    13. Wang, Xuejun & Hu, Shuhe & Yang, Wenzhi & Ling, Nengxiang, 2010. "Exponential inequalities and inverse moment for NOD sequence," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 452-461, March.
    14. He, Wei & Cheng, Dongya & Wang, Yuebao, 2013. "Asymptotic lower bounds of precise large deviations with nonnegative and dependent random variables," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 331-338.
    15. Yiqing Chen & Kam C. Yuen & Kai W. Ng, 2011. "Precise Large Deviations of Random Sums in Presence of Negative Dependence and Consistent Variation," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 821-833, December.
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    Cited by:

    1. 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.
    2. Wei Li & Pingyan Chen & Soo Hak Sung, 2016. "Complete Moment Convergence for Sung’s Type Weighted Sums of -Valued Random Elements," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-8, March.
    3. 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.
    4. Xin Deng & Xuejun Wang, 2018. "Asymptotic Property of M Estimator in Classical Linear Models Under Dependent Random Errors," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1069-1090, December.
    5. Xuejun Wang & Xin Deng & Shuhe Hu, 2018. "On consistency of the weighted least squares estimators in a semiparametric regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 797-820, October.
    6. Wenzhi Yang & Haiyun Xu & Ling Chen & Shuhe Hu, 2018. "Complete consistency of estimators for regression models based on extended negatively dependent errors," Statistical Papers, Springer, vol. 59(2), pages 449-465, June.
    7. Chen, Pingyan & Sung, Soo Hak, 2019. "A Spitzer-type law of large numbers for widely orthant dependent random variables," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    8. 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.
    9. Li Yongming & Li Naiyi & Luo Zhongde & Xing Guodong, 2024. "Asymptotic Behaviors of the VaR and CVaR Estimates for Widely Orthant Dependent Sequences," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-22, September.
    10. Yan, Ji Gao, 2018. "Complete Convergence and Complete Moment Convergence for Maximal Weighted Sums of Extended Negatively Dependent Random Variables," IRTG 1792 Discussion Papers 2018-040, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    11. Aiting Shen & Andrei Volodin, 2017. "Weak and strong laws of large numbers for arrays of rowwise END random variables and their applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 605-625, November.
    12. Liangxue Li & Xiaoqian Zheng & Haiwu Huang & Xuejun Wang, 2024. "Strong Convergence Properties for Weighted Sums of Extended Negatively Dependent Random Variables Under Sub-linear Expectations with Statistical Applications," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-36, September.
    13. Aiting Shen & Huiling Tao & Xuejun Wang, 2020. "The asymptotic properties for the estimators of the survival function and failure rate function based on WOD samples," Statistical Papers, Springer, vol. 61(6), pages 2671-2684, December.
    14. Yi Wu & Wei Yu & Xuejun Wang, 2022. "Strong representations of the Kaplan–Meier estimator and hazard estimator with censored widely orthant dependent data," Computational Statistics, Springer, vol. 37(1), pages 383-402, March.
    15. Xuejun Wang & Yi Wu & Rui Wang & Shuhe Hu, 2021. "On consistency of wavelet estimator in nonparametric regression models," Statistical Papers, Springer, vol. 62(2), pages 935-962, April.
    16. Xin Deng & Xuejun Wang, 2020. "An exponential inequality and its application to M estimators in multiple linear models," Statistical Papers, Springer, vol. 61(4), pages 1607-1627, August.

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