Estimation using double sampling and dual stratification - ARCHIVED

The problem considered is that of estimation of the total of a finite population which is stratified at two levels: a deeper level which has low intrastratum variability but is not known until the first phase of sampling, and a known pre-stratification which is relatively effective, unit by unit, in predicting the deeper post-stratification. As an important example, the post-stratification may define two groups corresponding to responders and non-responders in the situation of two-phase sampling for non-response. The estimators of Vardeman and Meeden (1984) are employed in a variety of situations where different types of prior information are assumed. In a general case, the standard error relative to that of the usual methods is studied via simulation. In the situation where no prior information is available and where proportional sampling is employed, the estimator is unbiased and its variance is approximated. Here, the variance is always lower than that of the usual double sampling for stratification. Also, without prior information, but with non-proportional sampling, using a slight modification of the second phase sampling plan, an unbiased estimator is found along with its variance, an unbiased estimator of its variance, and an optimal allocation scheme for the two phases of sampling. Finally, applications of these methods are discussed.