A Modified Post-stratified Regression Estimator for Two Occasions and using Two Variables

Post stratification is grouping of selected samples into sub-homogeneous strata and it is appropriate when there is lack of prior knowledge of stratifying variable. Many authors have worked on post stratified estimators by using one variable but very often this leads to high Mean Square Error (MSE) and low response rate. This work proposed a modified post stratified regression estimator by using two variables which are highly correlated for the purpose of minimizing the mean square error and increasing the response rate. In this study we proposed two post stratified estimators, a separate estimators and a combined regression estimators, which were then extended to estimate the un-matched part of the second occasion in two occasions sampling. The variances for both estimators were derived. The optimum variance for the second occasion in two occasions sampling were also obtained. These estimators were compared with existing estimators. The variances for the separate and combined estimators were 186,962,721 and 122,368,755 respectively, while for the existing were 336,189,459The optimum variance for the second occasion of the two occasion sampling for the separate and combined were 186,205,360 and 116,814,981 respectively while for the existing were 278,884,253. For the two data sets, it can be seen that the combine post stratified estimator were found to be more efficient (ratio 3:2) than separate post stratified regression estimators. It can be seen that the variances for the proposed estimators were lesser, hence it is more efficient.