SOME ALLOCATION IN MULTIVARIATE STRATIFIED SAMPLING UNDER COST FUNCTION USING MULTI-OBJECTIVE OPTIMIZATION

Abstract

The problem of allocation for multiple characteristics of interest in stratified sampling design is examined in this thesis. We use regression estimator for estimating the population mean of more than one characteristics in stratified sampling. We determine the sample size that minimize coefficients of variation of estimates of population means under deterministic and estimated, linear and nonlinear, cost functions. We propose a procedure to maximize the precision of more than one estimates of population means and minimize the variable cost of survey, jointly, under a given sample size. The additional condition is introduced on sample size to avoid over sampling and achieve minimum precision in each strata. The allocation problem in multivariate stratified sampling design is formulated in multi-objective integer nonlinear programming. The proposed multi-objective optimization methods are used to solve formulated allocation problem. A general method is proposed to solve allocation problem in multivariate stratified sampling. One data set is used to illustrate the procedure and compare the efficiency of allocation methods.