Receiver operating characteristic （ROC） curve is often used to study and compare two- sample problems in medicine. When more information may be available on one treatment than the other, one can improve estimator of...Receiver operating characteristic （ROC） curve is often used to study and compare two- sample problems in medicine. When more information may be available on one treatment than the other, one can improve estimator of ROC curve if the auxiliary population information is taken into account. The authors show that the empirical likelihood method can be naturally adapted to make efficient use of the auxiliary information to such problems. The authors propose a smoothed empirical likelihood estimator for ROC curve with some auxiliary information in medical studies. The proposed estimates are more efficient than those ROC estimators without any auxiliary information, in the sense of comparing asymptotic variances and mean squared error （MSE）. Some asymptotic properties for the empirical likelihood estimation of ROC curve are established. A simulation study is presented to demonstrate the performance of the proposed estimators.展开更多
Semivarying coefficient models are frequently used in statistical models.In this paper,under the condition that the coefficient functions possess different degrees of smoothness,a two-stepmethod is proposed.In the cas...Semivarying coefficient models are frequently used in statistical models.In this paper,under the condition that the coefficient functions possess different degrees of smoothness,a two-stepmethod is proposed.In the case,one-step method for the smoother coefficient functions cannot beoptimal.This drawback can be repaired by using the two-step estimation procedure.The asymptoticmean-squared error for the two-step procedure is obtained and is shown to achieve the optimal rate ofconvergence.A few simulation studies are conducted to evaluate the proposed estimation methods.展开更多
基金This research was partially supported by National Natural Science Funds for Distinguished Young Scholar under Grant No. 70825004 and National Natural Science Foundation of China （NSFC） under Grant No. 10731010, the National Basic Research Program under Grant No. 2007CB814902, Creative Research Groups of China under Grant No.10721101 and Shanghai University of Finance and Economics through Project 211 Phase III and Shanghai Leading Academic Discipline Project under Grant No. B803.
文摘Receiver operating characteristic （ROC） curve is often used to study and compare two- sample problems in medicine. When more information may be available on one treatment than the other, one can improve estimator of ROC curve if the auxiliary population information is taken into account. The authors show that the empirical likelihood method can be naturally adapted to make efficient use of the auxiliary information to such problems. The authors propose a smoothed empirical likelihood estimator for ROC curve with some auxiliary information in medical studies. The proposed estimates are more efficient than those ROC estimators without any auxiliary information, in the sense of comparing asymptotic variances and mean squared error （MSE）. Some asymptotic properties for the empirical likelihood estimation of ROC curve are established. A simulation study is presented to demonstrate the performance of the proposed estimators.
基金supported in part by the National Natural Science Foundation of China under Grant No. 10871072Shanxi's Natural Science Foundation of China under Grant No. 2007011014
文摘Semivarying coefficient models are frequently used in statistical models.In this paper,under the condition that the coefficient functions possess different degrees of smoothness,a two-stepmethod is proposed.In the case,one-step method for the smoother coefficient functions cannot beoptimal.This drawback can be repaired by using the two-step estimation procedure.The asymptoticmean-squared error for the two-step procedure is obtained and is shown to achieve the optimal rate ofconvergence.A few simulation studies are conducted to evaluate the proposed estimation methods.
