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Smoothed NPMLEs in nonparametric Poisson mixtures and beyond

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arxiv 2406.08808 v1 pith:XRRECOYK submitted 2024-06-13 math.ST stat.TH

Keunwoo Lim , Fang Han This is my paper · ORCID
classification math.STstat.TH
keywords nonparametricpoissonbeyonddiscussdistanceunderachieveconclusion
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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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