Approximate optimal allocation in repeated sampling from a finite population
Consider a finite population of size N. Let samples of size n be drawn on each of two occasions. On the first occasion, an auxiliary variable x is measured and on the second occasion the study variable y is measured. Let \(\bar Y\) be the population mean of y. For estimating \(\bar Y\), one considers the best linear unbiased combination of means for the matched and unmatched samples by minimising V(\(\hat{\bar Y})\) with respect to the sampling design on the second occasion. This optimum allocation depends on the population correlation coefficient \(\rho\) which is usually assumed to be known from past experience or pilot studies. The author estimates \(\rho\) from an initial matched sample and then an approximately optimum allocation is obtained for which the corresponding estimator is suggested. Under a bivariate normal superpopulation model assumption, this suggested estimator has model expected m.s.e. equal to the minimum model m.s.e. of any linear unbiased estimate apart from an error of order \(n^{-2}\).
best linear unbiased combination of means
scientific article; zbMATH DE number 3928077