Minimum Hellinger distance estimation for correlated errors

Joonsung Kang

doi:10.7465/jkdi.2019.30.1.219

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저널정보

한국데이터정보과학회
한국데이터정보과학회지 학술저널
한국데이터정보과학회지 제30권 제1호
2019.1 219 - 231 (13page)
DOI : 10.7465/jkdi.2019.30.1.219

저자정보

Joonsung Kang (Gangneung-Wonju National University)

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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 influence 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.

#Cochrane-Orcutt estimation #M-estimation #minimum Hellinger distance #nonparametric density estimation #robust regression