**Sankhya: The Indian Journal of Statistics**

1996, Volume 58, Series A, Pt. 2, pp. 273--282

**ESTIMATION OF REGRESSION COEFFICIENTS SUBJECT TO INTERVAL CONSTRAINTS**

By

H. TOUTENBURG, *University of Munich*

and

V. K. SRIVASTAVA, *University of Lucknow*

SUMMARY. In this paper, we have postulated a linear regression model which is subject to a set of interval constraints on its regression coefficients. Recognizing that it is generally difficult to derive explicit expressions for the estimators of regression coefficients and to study their properties, two alternative formulations of constraints (one in the form of ellipsoidal restrictions and the other in the form of linear stochastic restrictions) are considered and efficiency properties of the resulting estimators are studied employing the small disturbance asymptotic theory.

*AMS (1990) subject classification.* 62J05.

*Key words and phrases.* Interval constraints, linear regression, minimax method, mixed method.