The expected mean squares for unbalanced mixed effect interactive model were derived using Brute Force Method. From the expected mean squares, there are no obvious denominators for testing for the main effects when th...The expected mean squares for unbalanced mixed effect interactive model were derived using Brute Force Method. From the expected mean squares, there are no obvious denominators for testing for the main effects when the factors are mixed. An expression for F-test for testing for the main effects was derived which was proved to be unbiased.展开更多
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
文摘The expected mean squares for unbalanced mixed effect interactive model were derived using Brute Force Method. From the expected mean squares, there are no obvious denominators for testing for the main effects when the factors are mixed. An expression for F-test for testing for the main effects was derived which was proved to be unbiased.
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.
