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

摘要

We consider the problem of unbiased estimation of a finite population proportion and compare the unequal probability sampling strategies due to Hansen-Hurwitz, Horvitz-Thompson, Rao-Hartley-Cochran and Midzuno-Sen under a super-population model. It is shown that the model expected variance is least for the Midzuno-Sen 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.