This paper sheds light on all open problem put forward by Cochran[1]. The comparison between two commonly used variance estimators v1(^R) and v2(^R) of the ratio estimator R for population ratio R from small sample se...This paper sheds light on all open problem put forward by Cochran[1]. The comparison between two commonly used variance estimators v1(^R) and v2(^R) of the ratio estimator R for population ratio R from small sample selected by simple random sampling is made following the idea of the estimated loss approach (See [2]). Considering the superpopulation model under which the ratio estimator ^-YR for population mean -Y is the best linear unbiased one, the necessary and sufficient conditions for v1(^R) v2(^R) and v2(^R) v1(^R) are obtained with ignored the sampling fraction f. For a substantial f, several rigorous sufficient conditions for v2(^R) v1(^R) are derived.展开更多
基金the National Natural Science Foundation of China (No.10071091)
文摘This paper sheds light on all open problem put forward by Cochran[1]. The comparison between two commonly used variance estimators v1(^R) and v2(^R) of the ratio estimator R for population ratio R from small sample selected by simple random sampling is made following the idea of the estimated loss approach (See [2]). Considering the superpopulation model under which the ratio estimator ^-YR for population mean -Y is the best linear unbiased one, the necessary and sufficient conditions for v1(^R) v2(^R) and v2(^R) v1(^R) are obtained with ignored the sampling fraction f. For a substantial f, several rigorous sufficient conditions for v2(^R) v1(^R) are derived.
