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

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

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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.

作者 Gang YU Wei GAO Ningzhong SHI

机构地区 School of Economics School of Mathematics and Quantitative Economics Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics

出处《Journal of Mathematical Research with Applications》 CSCD 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)

关键词 empirical likelihood maximum empirical likelihood estimation （MELE） concaveconvex function Lagrange multiplier saddle point. 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 [化学工程]