In this paper,a partially linear single-index model is investigated,and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested.It is proved that the proposed statistics a...In this paper,a partially linear single-index model is investigated,and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested.It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions,and hence can be used to construct the confidence regions of the parameters.Our methods can also deal with the confidence region construction for the index in the pure single-index model.A simulation study indicates that,in terms of coverage probabilities and average areas of the confidence regions,the proposed methods perform better than the least-squares method.展开更多
A partially linear model with longitudinal data is considered,empirical likelihood to infer-ence for the regression coefficients and the baseline function is investigated,the empirical log-likelihood ratios is proven ...A partially linear model with longitudinal data is considered,empirical likelihood to infer-ence for the regression coefficients and the baseline function is investigated,the empirical log-likelihood ratios is proven to be asymptotically chi-squared,and the corresponding confidence regions for the pa-rameters of interest are then constructed.Also by the empirical likelihood ratio functions,we can obtain the maximum empirical likelihood estimates of the regression coefficients and the baseline function,and prove the asymptotic normality.The numerical results are conducted to compare the performance of the empirical likelihood and the normal approximation-based method,and a real example is analysed.展开更多
The missing response problem in single-index models is studied, and a bias-correction method to infer the index coefficients is developed. Two weighted empirical log-likelihood ratios with asymptotic chisquare are der...The missing response problem in single-index models is studied, and a bias-correction method to infer the index coefficients is developed. Two weighted empirical log-likelihood ratios with asymptotic chisquare are derived, and the corresponding empirical likelihood confidence regions for the index coefficients are constructed. In addition, the estimators of the index coefficients and the link function are defined, and their asymptotic normalities are proved. A simulation study is conducted to compare the empirical likelihood and the normal approximation based method in terms of coverage probabilities and average lengths of confidence intervals. A real example illustrates our methods.展开更多
基金supported by the Natural Science Foundation of Beijing City(Grant No.1042002)Technology Development Plan Project of Beijing Education Committee(Grant No.KM200510005009)+1 种基金the Special Grants of Beijing for Talents(Grant No.20041D0501515)supported by a grant from the Research Grants Council of Hong Kong,Hong Kong(Grant No.HKU7060/04P).
文摘In this paper,a partially linear single-index model is investigated,and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested.It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions,and hence can be used to construct the confidence regions of the parameters.Our methods can also deal with the confidence region construction for the index in the pure single-index model.A simulation study indicates that,in terms of coverage probabilities and average areas of the confidence regions,the proposed methods perform better than the least-squares method.
基金The first author was supported by the National Natural Science Foundation of China(Grant No.10571008)the Natural Science Foundation of Beijing(Grant No.1072004)+1 种基金the Science and Technology Development Project of Education Committee of Beijing City(Grant No.KM200510005009)The second author was supported by a grant of the Research Grant Council of Hong Kong(Grant No.HKBU7060/04P)
文摘A partially linear model with longitudinal data is considered,empirical likelihood to infer-ence for the regression coefficients and the baseline function is investigated,the empirical log-likelihood ratios is proven to be asymptotically chi-squared,and the corresponding confidence regions for the pa-rameters of interest are then constructed.Also by the empirical likelihood ratio functions,we can obtain the maximum empirical likelihood estimates of the regression coefficients and the baseline function,and prove the asymptotic normality.The numerical results are conducted to compare the performance of the empirical likelihood and the normal approximation-based method,and a real example is analysed.
基金supported by National Natural Science Foundation of China(Grant Nos.11571025 and 11331011)the BCMIIS,the Ph D Program Foundation of Ministry of Education of China(Grant No.20121103110004)the Beijing Natural Science Foundation(Grant Nos.1142003 and L140003)
文摘The missing response problem in single-index models is studied, and a bias-correction method to infer the index coefficients is developed. Two weighted empirical log-likelihood ratios with asymptotic chisquare are derived, and the corresponding empirical likelihood confidence regions for the index coefficients are constructed. In addition, the estimators of the index coefficients and the link function are defined, and their asymptotic normalities are proved. A simulation study is conducted to compare the empirical likelihood and the normal approximation based method in terms of coverage probabilities and average lengths of confidence intervals. A real example illustrates our methods.
