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Minimum Hellinger distance estimation for correlated errors
Journal of the Korean Data & Information Science Society 2019;30:219-31
Published online January 31, 2019;  https://doi.org/10.7465/jkdi.2019.30.1.219
© 2019 Korean Data and Information Science Society.

Joonsung Kang1

1Department of Information Statistics, Gangneung-Wonju National University
Correspondence to: Associate professor, Department of Information Statistics, Gangneung-Wonju National University, Jukheon-gil 7, Gangneung-si, Korea. E-mail: mkang@gwnu.ac.kr
Received December 12, 2018; Revised December 31, 2018; Accepted January 4, 2019.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
A linear regression with correlated errors appears in many contexts. A linear regression assumes independent errors in the model but in reality, it is often violated. As a result, correlated errors can severely have an wrong in uence on robustness of the linear regression model. Robustness of parameter estimators in the linear regression model can be kept by using M-estimator. It, however, gets robustness at the sake of efficiency whereas minimum Hellinger distance (MHD) estimators attains both robustness and efficiency. In this paper, a newly-presented method is suggested to get the minimum Hellinger distance estimator for the linear regression with correlated errors. It requires an appropriate nonparametric kernel density estimation for correlated data to accomodate a cross-validation estimator. Simulation study and real data study are conducted for the model. In simulation study, the proposed method in the linear regression model with correlated errors presents smaller biases and mean squared errors than M-estimation and the adjusted least squares (ALS) estimation. In real data, the proposed method has smaller standard errors than the other two methods.
Keywords : Cochrane-Orcutt estimation, M-estimation, minimum Hellinger distance, nonparametric density estimation, robust regression.