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Asymptotic Property of M Estimator in Classical Linear Models Under Dependent Random Errors

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  • Xin Deng

    (Anhui University)

  • Xuejun Wang

    (Anhui University)

Abstract

In this paper, we first establish a useful result on strong convergence for weighted sums of widely orthant dependent (WOD, in short) random variables. Based on the strong convergence that we established and the Bernstein type inequality, we investigate the strong consistency of M estimators of the regression parameters in linear models based on WOD random errors under some more mild moment conditions. The results obtained in the paper improve and extend the corresponding ones for negatively orthant dependent random variables and negatively superadditive dependent random variables. Finally, the simulation study is provided to illustrate the feasibility of the theoretical result that we established.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:4:d:10.1007_s11009-017-9589-9
    DOI: 10.1007/s11009-017-9589-9
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    References listed on IDEAS

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    1. Liu, Li, 2009. "Precise large deviations for dependent random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1290-1298, May.
    2. Cheng, Ching-Shui & Li, Ker-Chau, 1984. "The strong consistency of M-estimators in linear models," Journal of Multivariate Analysis, Elsevier, vol. 15(1), pages 91-98, August.
    3. 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.
    4. Radhakrishna Rao, C. & Zhao, LC., 1992. "On the consistency of M-estimate in a linear model obtained through an estimating equation," Statistics & Probability Letters, Elsevier, vol. 14(1), pages 79-84, May.
    5. 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.
    6. 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.
    7. Chen, X. R. & Wu, Y. H., 1988. "Strong consistency of M-estimates in linear models," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 116-130, October.
    8. 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.
    9. Cui, Hengjian & He, Xuming & Ng, Kai W., 2004. "M-estimation for linear models with spatially-correlated errors," Statistics & Probability Letters, Elsevier, vol. 66(4), pages 383-393, March.
    10. Tingting Liu & Xuejun Wang & Xinghui Wang & Shuhe Hu, 2016. "On the exponential inequalities for widely orthant-dependent random variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(19), pages 5848-5856, October.
    11. 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.
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