Minimax Purposive Survey Sampling Design

Abstract

The linear regression superpopulation model for survey sampling allows a formulation of the survey design problem which is close to optimum experimental design theory. This article introduces an alternative criterion to that of Royall (1970). A sampling design can be chosen to minimize the maximum mean squared error (mse) of “prediction” over the unsampled units. An upper bound for this maximum mse is derived and an algorithm given for obtaining samples satisfying the bound. The efficiency of these minimax designs for estimation of the population total is compared with the best designs in this case—namely the balanced designs of Royall.

Key Words:

• Survey sampling
• Optimum design
• Superpopulations