A note on two variance estimators for Rao-hartley cochran estimator
Arijit Chaiudhuri, Joydip Mitra · Communication in Statistics- Theory and Methods · 1992
Rao, Hartley and Cochran (RHC, in brief) (1962) gave a useful method of sample selection with unequal probabilities from a finite population and an unbiased estimator for the population total along with a uniformly non-negative unbiased estimator for its variance. Ohlsson (1989) has recently proposed and recommended an alternative variance estimator as an improvement upon RHC's variance estimator numerically demonstrating higher efficiency of the former. RHC scheme of sampling involves formation of as many random groups as is the sample-size. Also RHC themselves showed that their estimator achieves the least variance when each of a set of groups has a common size while each of the complementary set of groups has another common size differing from the former by one. Observing that this is the only natural situation when one should consider the relative efficiencies of the above two variance estimators we numerically demonstrate that the magnitudes of the variances of these variance estimators differ little from each other and their differences may be both positive and negative. Hence there should be little to choose between the two in practice.