Approximate optimal allocation in repeated sampling from a finite population

Abstract

Abstract Samples of size n are drawn from a finite population on each of two occasions. On the first occasion a variate x is measured, and on the second a variate y . In estimating the population mean of y , the variance of the best linear unbiased combination of means for matched and unmatched samples is itself minimized, with respect to the sampling design on the second occasion, by a certain degree of matching. This optimal allocation depends on the population correlation coefficient, which previous authors have assumed known. We estimate the correlation from an initial matched sample, then an approximately optimal allocation is completed and an estimator formed which, under a bivariate normal superpopulation model, has model expected mean square error equal, apart from an error of order n -2 , to the minimum enjoyed by any linear, unbiased estimator.