Empirical Likelihood Estimation for the Two-Sample Mean under Density Ratio Models Using Auxiliary Information |
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Authors: | LI Huapeng LIU Yang |
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Institution: | School of Mathematics and Statistics, Shanxi Datong University, Datong, 037009, China; School of Statistics, East China Normal University, Shanghai, 200062, China |
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Abstract: | Auxiliary population information is often available in finite population inference problems, and the empirical likelihood (EL) approach has been demonstrated to be flexible and useful for such problems. The present paper concerns EL when interest centers on inference for the mean of the baseline distribution under two-sample density ratio models. Although dual EL is a convenient technical tool since it has the same maximum point and maximum likelihood as DRM-based EL, it can not combine such auxiliary information into the likelihood conveniently and may have loss of efficiency. By contrast, the classical EL approach of Qin and
Lawless\ucite{21} does not have this problem and incorporate seamlessly auxiliary information. Based on the EL using auxiliary information and the
dual EL methods, we construct both point and interval estimations and make a careful comparison. Though the point estimation efficiency gain obtained
by the former is not noticeable, we find that they may have different performances in interval estimation. In terms of coverage accuracy, the two intervals are comparable for not or moderate skewed populations, and the EL interval using auxiliary information can be much superior for severely skewed populations. |
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Keywords: | auxiliary information coverage accuracy empirical likelihood density ratio model dual likelihood |
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