Polylogarithmic Sparsity of Randomly Reweighted NPMLEs for Gaussian Mixtures
The nonparametric maximum likelihood estimator (NPMLE) of a Gaussian location mixture maximizes the likelihood over the infinite-dimensional space of mixing distributions. The maximizing mixing distribution can be nonunique, and the classical bound on its number of atoms grows linearly with the sample size $n$. We show that a vanishingly small random perturbation of the likelihood yields exact polylogarithmic sparsity. The resulting randomly reweighted NPMLE maximizes a weighted likelihood whose independent weights, taken to be Gamma in our analysis, concentrate around one as $n$ grows. With high probability, it is unique, has $O\{(\log n/\log\log n)^d+\log n\}$ atoms in dimension $d$, ne...
| Authors | Hansheng Jiang |
|---|---|
| Primary category | stat.ME |
| Published | 1 October 2026 |
| Last updated at source | 1 October 2026 |
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