Some Estimators Better Than Regression Estimator For a Finite Population
by
V. Dubey
Pt.Ravishankar Shukla university, Raipur(M.P),India
Coauthors: T. P. Tripathi (Indian Statistical Institute, Calcutta, India)

In case of bivariate finite populations where the mean [`X] of an auxiliarycharacteristics x is known, it is customary to define ratio, regression, product and difference estimators for estimating mean [`Y]of a principal variable y. It is well known that for large samples the mean squared error (MSE) of regression estimator is smaller than those of other estimators mentioned above. In this paper, we make a saerch for some estimators whose MSE may be smaller than that of regression estimator. For estimating [`Y] we considered several estimators of the form

d=(1-w) y   rg  + wt

where [`y]_rg is well known regression estimator, w is a suitably chosen weight and t is a function of y and x values in the sample. We have obtained optimum choices of weights w and corresponding minimum mean squared errors. The results are illustrated for bivariate normal populations. The relative efficiencies of the proposed estimators compared to that of regression estimator have been obtained for a natural population data.

Date received: November 15, 2000