Statistical Inference for Random Unknowns via Modifications of Extended Likelihood
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915175938916352 |
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| author | Lee, Hangbin Lee, Youngjo |
| author_facet | Lee, Hangbin Lee, Youngjo |
| contents | Fisher's likelihood is widely used for statistical inference for fixed unknowns. This paper aims to extend two important likelihood-based methods, namely the maximum likelihood procedure for point estimation and the confidence procedure for interval estimation, to embrace a broader class of statistical models with additional random unknowns. We propose the new h-likelihood and the h-confidence by modifying extended likelihoods. Maximization of the h-likelihood yields both maximum likelihood estimators of fixed unknowns and asymptotically optimal predictors for random unknowns, achieving the generalized Cramér-Rao lower bound. The h-likelihood further offers advantages in scalability for large datasets and complex models. The h-confidence could yield a valid interval estimation and prediction by maintaining the coverage probability for both fixed and random unknowns in small samples. We study approximate methods for the h-likelihood and h-confidence, which can be applied to a general class of models with additional random unknowns. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_09955 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Statistical Inference for Random Unknowns via Modifications of Extended Likelihood Lee, Hangbin Lee, Youngjo Statistics Theory Methodology Fisher's likelihood is widely used for statistical inference for fixed unknowns. This paper aims to extend two important likelihood-based methods, namely the maximum likelihood procedure for point estimation and the confidence procedure for interval estimation, to embrace a broader class of statistical models with additional random unknowns. We propose the new h-likelihood and the h-confidence by modifying extended likelihoods. Maximization of the h-likelihood yields both maximum likelihood estimators of fixed unknowns and asymptotically optimal predictors for random unknowns, achieving the generalized Cramér-Rao lower bound. The h-likelihood further offers advantages in scalability for large datasets and complex models. The h-confidence could yield a valid interval estimation and prediction by maintaining the coverage probability for both fixed and random unknowns in small samples. We study approximate methods for the h-likelihood and h-confidence, which can be applied to a general class of models with additional random unknowns. |
| title | Statistical Inference for Random Unknowns via Modifications of Extended Likelihood |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2310.09955 |