Estimation of Population Total in Two Stage Design with PPS Sampling and Using Double Sampling for Auxiliary Information

This paper proposes multivariate Difference and Ratio estimators for estimation of population total in two-stage design when the required auxiliary information is unavailable and is collected either at fsu level or at ssu level for selecting the probabilities as well as for estimating population total. Variance of the proposed estimators are derived. Optimum estimators with minimum variance are obtained.