ESTIMATING VARIANCE IN THE PRESENCE OF NONRESPONSE UNDER UNEQUAL PROBABILITY SAMPLING WITHOUT REPLACEMENT

In this paper we propose 2 estimators for estimating a population total under unequal probability sampling without replacement, a linear and a ratio estimator. We show in theory that the linear estimator is an unbiased estimator and the latter is an asymptotically unbiased estimator. We propose a general form of the variance, and also an estimator of the variance in this paper considered under the reverse framework and only when the sampling fraction is negligible. We can show in theory that the variance estimators of the proposed estimators are asymptotically unbiased. A simulation study has been conducted to ascertain the performance of the proposed estimators.