Comparisons of sampling strategies for estimating finite population proportions in direct and randomized response surveys under a super population model

Abstract

We consider the problem of unbiased estimation of a finite population proportion and compare the unequal probability sampling strategies due to Hansen-Hurwitz (9), Horvitz-Thompson (12), Rao-Hartley-Cochran (18) and Midzuno-Sen (16,20) under a super-population model. It is shown that the model expected variance is least for the Midzuno-Sen (16,20) strategy both when these sampling strategies are based on data obtained from (i) a direct survey and (ii) a randomized response (RR) survey employing some RR technique following a general RR model.