Preliminary Test Estimators in Double Sampling

It is known that in many of the large scale surveys,it is inevitable to adopt stratification for the purpose of preparing a frame from which the sample can be extracted. Cochran (1977) suggested a regression estimate in stratified sampling which he called a combined regression estimate. In the present study, situations will be considered where partial information about the mean of the auxiliary variable is available. In order to utilize the partial information, double sampling is used and a preliminary test is done to construct the combined regression preliminary test estimator. The bias, mean square error and the relative efficiency are obtained for the suggested estimator. Apart from analytical results, these are also obtained by numerical techniques. The comparative study shows the the bias and the mean square error function obtained by numerical methods depict similar pattern with that obtained by analytical methods. In order to judge the performance of the suggested estimator, empirical work is also carried out with the help of both real as well as simulated data. Recommendation of the levels of the preliminary test and optimum allocation of sample sizes are given.