| Abstract: | It is well known for direct response surveys (DR), where the responses are obtained from the respondents directly, that the sample mean, based on distinct units of a simple random sample selected with replacement (SRSWR) method, is more efficient than the sample mean based on all the units including repetition. In this paper, it is shown that a linear unbiased estimator based on distinct units is inadmissible for estimating a finite population mean when the sample is selected by an arbitrary with replacement (WR) sampling scheme and the responses are obtained independently by some RR technique. Efficiencies for a few linear unbiased estimators are compared under SRSWR sampling. |
