**Sankhya: The Indian Journal of Statistics**

1996, Volume 58, Series B, Pt. 3, pp. 352--359

**THE LINEAR ZERO FUNCTIONS APPROACH TO LINEAR MODELS**

By

PAWELR PORDZIK , *Agricultural University of Poznan, Poznan*

and

GÖTZ TRENKLER, *University of Dortmund, Dortmund*

SUMMARY. Consider the standard regression model $y= X\beta +\eta$ and two sets of computing non exact linear restrictions $R_i\beta_{i} = r_{i}$, i=1, 2. Necessary and sufficient conditions are derived under which one of the restricted least squares estimator of $\beta$ dominates the other in the sense of mean square error matrix.

*AMS (1991) subject classification.* 65F15.

*Key words and phrases.* Linear regression model, linear restrictions, mean square error matrix comparisons.