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.

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