Optimal estimation for finite population parameters in two phase sampling.

In this paper we propose a general approh for estimating a finite population parameter in double sampling. When two dependent samples are drawn, several estimators were proposed to estimate the population me, ratio and variance. While there are few proposals in double sampling with independent samples. We treat both cases, i.e. dependent and independent samples, showing that all the proposed estimators can be obtained as particular cases of a unique general class. The minimum variance bound for any estimator in this class is provided (at the first order of approximation). Furthermore, a chain regression type estimator which reaches this minimum is found.