Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series B, Pt. 1, pp. 1--10

OPTIMAL PREDICTION OF THE FINITE POPULATION REGRESSION COEFFICIENT

By

H. BOLFARINE, S. ZACKS, S. N. ELIAN and J. RODRIGUES, *University of Sao Paolo and State University of New York, Binghamton*

SUMMARY. In this paper we investigate optimal prediction of the finite population regression coefficient **b **_{N} under a general linear regression superpopulation model. Optimal predictors are obtained under Gaussian superpopulation models and also under weaker Gauss-Markov type assumptions. We derive the optimum linear predictor of **b **_{N} under the general linear model with a nondiagonal covariance matrix and show that it reduces to the usual least squares estimator of the superpopulation regression coefficient.

*AMS (1990) subject classification.* 62D05.

*Key words and phrases.* Best linear predictor, best unbiased predictor regression coefficient, two stage sampling, weighted least squares.