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Asymptotic properties of LS estimators in the errors-in-variables model with MD errors

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  • Aiting Shen

    (Anhui University)

Abstract

In this paper, the complete convergence for weighted sums of a class of random variables is established. By using the complete convergence, we further investigate the complete consistency of LS estimators in the EV regression model with martingale difference (in short) errors. In addition, the mean consistency of LS estimators is also studied. The results obtained in the paper generalize the corresponding ones for independent random variables and some dependent random variables.

Suggested Citation

  • Aiting Shen, 2019. "Asymptotic properties of LS estimators in the errors-in-variables model with MD errors," Statistical Papers, Springer, vol. 60(4), pages 1193-1206, August.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:4:d:10.1007_s00362-016-0869-1
    DOI: 10.1007/s00362-016-0869-1
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    References listed on IDEAS

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    1. Yu Miao & Fangfang Zhao & Ke Wang & Yanping Chen, 2013. "Asymptotic normality and strong consistency of LS estimators in the EV regression model with NA errors," Statistical Papers, Springer, vol. 54(1), pages 193-206, February.
    2. Xuejun Wang & Shuhe Hu & Wenzhi Yang & Xinghui Wang, 2012. "Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, July.
    3. Xuejun Wang & Aiting Shen & Zhiyong Chen & Shuhe Hu, 2015. "Complete convergence for weighted sums of NSD random variables and its application in the EV regression model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 166-184, March.
    4. Qunying Wu, 2012. "Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-10, July.
    5. Guo-Liang Fan & Han-Ying Liang & Jiang-Feng Wang & Hong-Xia Xu, 2010. "Asymptotic properties for LS estimators in EV regression model with dependent errors," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(1), pages 89-103, March.
    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. Anderson, T. W. & Kunitomo, Naoto, 1992. "Asymptotic distributions of regression and autoregression coefficients with martingale difference disturbances," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 221-243, February.
    8. Deaton, Angus, 1985. "Panel data from time series of cross-sections," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 109-126.
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