| A Note on the Estimation of Semiparametric Two-Sample Density Ratio Models |
| Received:August 08, 2010 Revised:January 13, 2011 |
| Key Words:
empirical likelihood maximum empirical likelihood estimation (MELE) concave-convex function Lagrange multiplier saddle point.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.10931002; 11071035; 70901016; 71171035) and Excellent Talents Program of Liaoning Educational Committee (Grant No.2008RC15). |
| Author Name | Affiliation | | Gang YU | 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 | | Wei GAO | Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics, Northeast Normal University, Jilin 130024, P. R. China | | Ningzhong SHI | 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2012.02.005 |
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