Optimum stratified sampling using prior information

The stratified sample allocation problem using prior information concerning strata variances, is considered. Given k random variables Xi, X2, • • •, Xk on a probability space, a Borel measurable function X of Xi, X2, • • •, X^, called a maximal utility function, is defined. A rigorous derivation of its expected value is presented. The definition and expected value of X are repeatedly used to formulate the objective functions used to solve the stratified sample allocation problem. The resulting allocations are called minimax allocations. Assuming prior information in the form of a distribution function on strata variances, a noninformative design which happens to be an alternative to Aggarwal's (1958) allocation, is proposed. If prior information concerning strata coefficients of variation is available, a minimax sampling strategy based on Searis' (1964) work, is presented. Under a normal superpopulation model, assuming locally uniform prior distributions on strata means and variances, two-phase minimax allocations comparable with that of Draper et al. (1968) are developed. Several numerical examples are given to illustrate and compare minimax allocation procedure with other existing procedures.