Smoothed NPMLEs in nonparametric Poisson mixtures and beyond
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913390049361920 |
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| author | Lim, Keunwoo Han, Fang |
| author_facet | Lim, Keunwoo Han, Fang |
| contents | We discuss nonparametric mixing distribution estimation under the Gaussian-smoothed optimal transport (GOT) distance. It is shown that a recently formulated conjecture -- that the Poisson nonparametric maximum likelihood estimator can achieve root-$n$ rate of convergence under the GOT distance -- holds up to some logarithmic terms. We also establish the same conclusion for other minimum-distance estimators, and discuss mixture models beyond the Poisson. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08808 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Smoothed NPMLEs in nonparametric Poisson mixtures and beyond Lim, Keunwoo Han, Fang Statistics Theory We discuss nonparametric mixing distribution estimation under the Gaussian-smoothed optimal transport (GOT) distance. It is shown that a recently formulated conjecture -- that the Poisson nonparametric maximum likelihood estimator can achieve root-$n$ rate of convergence under the GOT distance -- holds up to some logarithmic terms. We also establish the same conclusion for other minimum-distance estimators, and discuss mixture models beyond the Poisson. |
| title | Smoothed NPMLEs in nonparametric Poisson mixtures and beyond |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2406.08808 |