Asymptotically design-unbiased predictors in survey sampling

SUMMARY A probability sampling plan is suggested in this paper for drawing the sample so that the linear least-squares predictor of the total of a finite population is made asymptotically design-unbiased. Conditions are given for the sampling plan to reduce to the more familiar sample designs discussed in the literature. The linear least-squares predictor of the total of a finite population (Royall, 1970, 1976) derived under a superpopulation model with explanatory variables omitted is still best under the correct model provided that it is unbiased under the correct model (Tam, 1986). The present paper specifies probability sampling schemes which render the linear least-squares predictor asymptoti- cally design-unbiased. Such probability schemes enable some general form of balancing in the sample for the explanatory variables omitted from the assumed superpopulation model, and provide protection of the predictor against this type of model failure. Conditions are also presented in this paper for the specified sample design to become the equal probability selection sample design or the optimal sample design considered by Godambe (1955, 1982).