Asymptotic bias reduction of maximum likelihood estimates via penalized likelihoods with differential geometry
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866914726589497344 |
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| author | Hirose, Masayo Y. Mano, Shuhei |
| author_facet | Hirose, Masayo Y. Mano, Shuhei |
| contents | A procedure for asymptotic bias reduction of maximum likelihood estimates of generic estimands is developed. The estimator is realized as a plug-in estimator, where the parameter maximizes the penalized likelihood with a penalty function that satisfies a quasi-linear partial differential equation of the first order. The integration of the partial differential equation with the aid of differential geometry is discussed. Applications to generalized linear models, linear mixed-effects models, and a location-scale family are presented. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2011_14747 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Asymptotic bias reduction of maximum likelihood estimates via penalized likelihoods with differential geometry Hirose, Masayo Y. Mano, Shuhei Statistics Theory 62F12, 62B11, 62H12 A procedure for asymptotic bias reduction of maximum likelihood estimates of generic estimands is developed. The estimator is realized as a plug-in estimator, where the parameter maximizes the penalized likelihood with a penalty function that satisfies a quasi-linear partial differential equation of the first order. The integration of the partial differential equation with the aid of differential geometry is discussed. Applications to generalized linear models, linear mixed-effects models, and a location-scale family are presented. |
| title | Asymptotic bias reduction of maximum likelihood estimates via penalized likelihoods with differential geometry |
| topic | Statistics Theory 62F12, 62B11, 62H12 |
| url | https://arxiv.org/abs/2011.14747 |