Double Sampling with Partial Information on Auxiliary Variables

Abstract

It is well known that the precision of an estimator can be improved if auxiliary variables are used. In particular, if the relationship is linear, a linear regression estimator is constructed. When the mean of the auxiliary variable is completely unknown, double sampling techniques can be adopted. If the experimenter has partial information about the mean, he may perform a preliminary test and construct a preliminary test estimator. The bias, mean square error and relative efficiency are obtained for the preliminary test estimator. Recommendation of the levels of the preliminary test and optimum allocation of sample sizes are given. When the prior distribution of the mean of the auxiliary variable is normal, a maximum likelihood estimator is obtained.