Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series B, Pt. 3, pp. 433-442

ESTIMATION OF REGRESSION COEFFICIENTS SUBJECT TO INTERVAL CONSTRAINTS IN MODELS WITH NON-SPHERICAL ERRORS

By

ANOOP CHATURVEDI, * University of Allahabad, Allahabad*

and

ALAN T.K. WAN, *City University of Hong Kong, Hong Kong*

*SUMMARY.* This article considers the formulation of interval restrictions as a concentration ellipsoid or
as stochastic linear restrictions, in the context of a linear model with non-spherical
disturbances and unknown covariance matrix for the disturbances. We derive the
asymptotic distributions of the estimators arising from the two alternative formulations,
and establish the dominance conditions of one estimator over the other with respect to the
mean squared error matrix and risk under quadratic loss criteria. Our results improve
earlier results of Toutenburg and Srivastava (1996) which assume that the disturbances'
covariance matrix is known except for a scalar multiple. A simulation study is conducted
to examine the small sample behaviour of the estimators.

*AMS (1991) subject classification.*62J05.

*Key words and phrases. *Asymptotic, interval constraints, linear regression, mean squared
error, minimax method, mixed regression, quadratic loss, risk