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Asymptotic Normality of M-Estimator in Linear Regression Model with Asymptotically Almost Negatively Associated Errors

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  • Yu Zhang

    (School of Mathematics and Statistics, Bigdata Modeling and Intelligent Computing Research Institute, Hubei University of Education, Wuhan 430205, China)

Abstract

This paper studies a linear regression model in which the errors are asymptotically almost negatively associated (AANA, in short) random variables. Firstly, the central limit theorem for AANA sequences of random variables is established. Then, we use the central limit theorem to investigate the asymptotic normality of the M-estimator for the unknown parameters. Some results for independent and negatively associated (NA, in short) random variables are extended to the case of AANA setting. Finally, a simulation is carried out to verify the asymptotic normality of the M-estimator in the model.

Suggested Citation

  • Yu Zhang, 2023. "Asymptotic Normality of M-Estimator in Linear Regression Model with Asymptotically Almost Negatively Associated Errors," Mathematics, MDPI, vol. 11(18), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3858-:d:1236387
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    References listed on IDEAS

    as
    1. Kouritzin, Michael A. & Paul, Sounak, 2022. "On almost sure limit theorems for heavy-tailed products of long-range dependent linear processes," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 208-232.
    2. Hongchang Hu & Yu Zhang & Xiong Pan, 2016. "Asymptotic normality of DHD estimators in a partially linear model," Statistical Papers, Springer, vol. 57(3), pages 567-587, September.
    3. Xueping Hu & Guohua Fang & Dongjin Zhu, 2012. "Strong Convergence Properties for Asymptotically Almost Negatively Associated Sequence," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-8, October.
    4. Butzer, P. L. & Hahn, L., 1978. "General theorems on rates of convergence in distribution of random variables I. General limit theorems," Journal of Multivariate Analysis, Elsevier, vol. 8(2), pages 181-201, June.
    5. Yu Zhang & Xinsheng Liu & Hongchang Hu, 2020. "Weak consistency of M-estimator in linear regression model with asymptotically almost negatively associated errors," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(11), pages 2800-2816, June.
    6. 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.
    7. Shuyang Bai & Murad S. Taqqu, 2013. "Multivariate Limit Theorems In The Context Of Long-Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 717-743, November.
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