AISM 52, 332-342

## 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}

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

^{2}Department 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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