Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series B, Pt. 3, 415--435

SOME ROBUST PROCEDURES FOR ESTIMATING PARAMETERS IN AN AUTOREGRESSIVE MODEL

By

W. Y. TAN,

And

VICKEY LIN, * Memphis State University, U.S.A*

SUMMARY. In this paper we develop some robust estimators for estimating regression coefficients in a simple model with autocorrelated errors. These robust estimators were derived by using the Winsorized method and the Tiku's MMLE method. Some Monte Carlo studies involving 5 different distributions indicate clearly that the modified Winsorized estimator and the Tiku's MMLE are more efficient than the Winsorized estimator in all cases. The robust estimators are considerably more efficient than the Durbin estimator and the $\L_1$ norm estimator when the universe is not normal, but are less efficient when the universe is normally distributed. To improve on the efficiency of the robust estimators under normal distribution, some adaptive estimators were derived. These adaptive estimators are almost as efficient as the Durbin estimator and the $\L_1$ norm estimator when the universe is normally distributed but are considerably more efficient when the universe is not normal.

*Subject classification*. 62M10