Optimum stratified sampling using prior information



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Texas Tech University


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.



Estimation theory, Statistical decision, Sampling (Statistics)