Level-specific correction for nonparametric likelihoods |
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| Authors: | Yukun Liu Jiahua Chen Ting Li |
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| Institution: | 1. School of Finance and Statistics, East China Normal University, 500 Dongchuan Road, Shanghai 200241, People's Republic of China;2. Department of Statistics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2 |
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| Abstract: | The popular empirical likelihood method not only has a convenient chi-square limiting distribution but is also Bartlett correctable, leading to a high-order coverage precision of the resulting confidence regions. Meanwhile, it is one of many nonparametric likelihoods in the Cressie–Read power divergence family. The other likelihoods share many attractive properties but are not Bartlett correctable. In this paper, we develop a new technique to achieve the effect of being Bartlett correctable. Our technique is generally applicable to pivotal quantities with chi-square limiting distributions. Numerical experiments and an example reveal that the method is successful for several important nonparametric likelihoods. |
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| Keywords: | Bartlett correction empirical likelihood exponential tilting likelihood Euclidean likelihood power divergence family |
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