We revisit a comparison of two discriminant analysis procedures, namely the linear combination classifier of Chung and Han (2000) and the maximum likelihood estimation substitution classifier for the problem of classi...We revisit a comparison of two discriminant analysis procedures, namely the linear combination classifier of Chung and Han (2000) and the maximum likelihood estimation substitution classifier for the problem of classifying unlabeled multivariate normal observations with equal covariance matrices into one of two classes. Both classes have matching block monotone missing training data. Here, we demonstrate that for intra-class covariance structures with at least small correlation among the variables with missing data and the variables without block missing data, the maximum likelihood estimation substitution classifier outperforms the Chung and Han (2000) classifier regardless of the percent of missing observations. Specifically, we examine the differences in the estimated expected error rates for these classifiers using a Monte Carlo simulation, and we compare the two classifiers using two real data sets with monotone missing data via parametric bootstrap simulations. Our results contradict the conclusions of Chung and Han (2000) that their linear combination classifier is superior to the MLE classifier for block monotone missing multivariate normal data.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We revisit a comparison of two discriminant analysis procedures, namely the linear combination classifier of Chung and Han (2000) and the maximum likelihood estimation substitution classifier for the problem of classifying unlabeled multivariate normal observations with equal covariance matrices into one of two classes. Both classes have matching block monotone missing training data. Here, we demonstrate that for intra-class covariance structures with at least small correlation among the variables with missing data and the variables without block missing data, the maximum likelihood estimation substitution classifier outperforms the Chung and Han (2000) classifier regardless of the percent of missing observations. Specifically, we examine the differences in the estimated expected error rates for these classifiers using a Monte Carlo simulation, and we compare the two classifiers using two real data sets with monotone missing data via parametric bootstrap simulations. Our results contradict the conclusions of Chung and Han (2000) that their linear combination classifier is superior to the MLE classifier for block monotone missing multivariate normal data.
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.
