Two-sample empirical likelihood method for difference between coefficients in linear regression model |
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Authors: | Xuemin Zi Changliang Zou Yukun Liu |
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Institution: | 1. Department of Mathematics, Tianjin University of Technology and Education, Tianjin, 300222, China 2. Department of Statistics, School of Mathematical Sciences, Nankai University, Tianjin, 300071, China 3. School of Finance and Statistics, East China Normal University, Shanghai, China
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Abstract: | The empirical likelihood method is proposed to construct the confidence regions for the difference in value between coefficients
of two-sample linear regression model. Unlike existing empirical likelihood procedures for one-sample linear regression models,
as the empirical likelihood ratio function is not concave, the usual maximum empirical likelihood estimation cannot be obtained
directly. To overcome this problem, we propose to incorporate a natural and well-explained restriction into likelihood function
and obtain a restricted empirical likelihood ratio statistic (RELR). It is shown that RELR has an asymptotic chi-squared distribution.
Furthermore, to improve the coverage accuracy of the confidence regions, a Bartlett correction is applied. The effectiveness
of the proposed approach is demonstrated by a simulation study. |
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