| 半参数两样本密度比率模型估计问题的一点注记 |
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| 引用本文： | 于刚,高巍,史宁中.半参数两样本密度比率模型估计问题的一点注记[J].数学研究及应用,2012,32(2):174-180. |
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| 作者姓名： | 于刚 高巍 史宁中 |
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| 作者单位： | 华中科技大学经济学院, 湖北 武汉 430074; 东北财经大学数学与数量经济学院, 辽宁 大连 116025;东北师范大学应用统计教育部重点实验室,数学与统计学院, 吉林 长春 130024;东北师范大学应用统计教育部重点实验室,数学与统计学院, 吉林 长春 130024 |
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| 基金项目： | 国家自然科学基金(Grant Nos.10931002;11071035;70901016;71171035), 辽宁省优秀人才支持计划项目(Grant No.2008RC15). |
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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.
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| 关 键 词： | empirical likelihood maximum empirical likelihood estimation (MELE) concaveconvex function Lagrange multiplier saddle point. |
| 收稿时间： | 8/8/2010 12:00:00 AM |
| 修稿时间： | 2011/1/13 0:00:00 |
A Note on the Estimation of Semiparametric Two-Sample Density Ratio Models |
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| Gang YU,Wei GAO and Ningzhong SHI.A Note on the Estimation of Semiparametric Two-Sample Density Ratio Models[J].Journal of Mathematical Research with Applications,2012,32(2):174-180. |
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| Authors: | Gang YU Wei GAO and Ningzhong SHI |
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| Institution: | School of Economics, Huazhong University of Science and Technology, Hubei 430074, P. R. China; School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Liaoning 116025, P. R. China;Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics, Northeast Normal University, Jilin 130024, P. R. China;Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics, Northeast Normal University, Jilin 130024, P. R. China |
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| Abstract: | 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 concave-convex 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. |
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| Keywords: | empirical likelihood maximum empirical likelihood estimation (MELE) concave-convex function Lagrange multiplier saddle point |
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