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arXiv · 2406.08808

Smoothed NPMLEs in nonparametric Poisson mixtures and beyond

Keunwoo Lim·Fang Han
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Abstract

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.

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Keunwoo Lim, Fang Han. 2024-06-13. Smoothed NPMLEs in nonparametric Poisson mixtures and beyond. https://arxiv.org/abs/2406.08808

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