OPERATIONAL VARIANTS OF THE MINIMUM MEAN SQUARED ERROR ESTIMATOR IN LINEAR REGRESSION MODELS WITH NON-SPHERICAL DISTURBANCES

ALAN T. K. WAN^{1} AND ANOOP CHATURVEDI^{2}

1Department of Management Sciences, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China

2Department of Mathematics and Statistics, University of Allahabad, Allahabad-211002, India

(Received July 13, 1998; revised October 26, 1998)

Abstract. There is a good deal of literature that investigates the properties of various operational variants of Theil’s (1971, Principles of Econometrics, Wiley, New York) minimum mean squared error estimator. It is interesting that virtually all of the existing analysis to date is based on the premise that the model’s disturbances are i.i.d., an assumption which is not satisfied in many practical situations. In this paper, we consider a model with non-spherical errors and derive the asymptotic distribution, bias and mean squared error of a general class of feasible minimum mean squared error estimators. A Monte-Carlo experiment is conducted to examine the performance of this class of estimators in finite samples.

Key words and phrases: Asymptotic expansion, quadratic loss, minimum mean squared error, risk, Stein-rule.

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