A Note on the Estimation of Semiparametric Two-Sample Density Ratio Models  

作　　者：Gang YU Wei GAO Ningzhong SHI 

机构地区：[1]School of Economics, Huazhong University of Science and Technology,Hubei 430074, P. R. China [2]School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Liaoning 116025, P. R. China [3]Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics, Northeast Normal University, Jilin 130024, P. R. China

出　　处：《Journal of Mathematical Research with Applications》2012年第2期174-180,共7页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant Nos. 10931002;11071035;70901016;71171035);Excellent Talents Program of Liaoning Educational Committee (Grant No. 2008RC15)

摘　　要：In this paper, a semiparametric two-sample density ratio model is considered and the empirical likelihood method is applied to obtain the parameters estimation. A commonly occurring problem in computing is that the empirical likelihood function may be a concaveconvex function. Here a simple Lagrange saddle point algorithm is presented for computing the saddle point of the empirical likelihood function when the Lagrange multiplier has no explicit solution. So we can obtain the maximum empirical likelihood estimation （MELE） of parameters. Monte Carlo simulations are presented to illustrate the Lagrange saddle point algorithm.In this paper, a semiparametric two-sample density ratio model is considered and the empirical likelihood method is applied to obtain the parameters estimation. A commonly occurring problem in computing is that the empirical likelihood function may be a concaveconvex function. Here a simple Lagrange saddle point algorithm is presented for computing the saddle point of the empirical likelihood function when the Lagrange multiplier has no explicit solution. So we can obtain the maximum empirical likelihood estimation （MELE） of parameters. Monte Carlo simulations are presented to illustrate the Lagrange saddle point algorithm.

关 键 词：empirical likelihood maximum empirical likelihood estimation （MELE） concaveconvex function Lagrange multiplier saddle point. 

分 类 号：O212.1[理学—概率论与数理统计] TQ021.1[理学—数学]