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

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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.

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Acknowledgements

The authors are most grateful to the Editor-in-Chief Christine H. Müller and two anonymous referees for careful reading of the manuscript and valuable suggestions which helped in improving an earlier version of this paper. Supported by the National Natural Science Foundation of China (11501004, 11671012), the Natural Science Foundation of Anhui Province (1508085J06), the Provincial Natural Science Research Project of Anhui Colleges (KJ2015A018), Doctoral Research Start-up Funds Projects of Anhui University, the Quality Engineering Project of Anhui Province (2015jyxm045) and the Quality Improvement Projects for Undergraduate Education of Anhui University (ZLTS2015035).

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  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, People’s Republic of China

    Aiting Shen

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Shen, A. Asymptotic properties of LS estimators in the errors-in-variables model with MD errors. Stat Papers 60, 1193–1206 (2019). https://doi.org/10.1007/s00362-016-0869-1

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