Preprint
Oct 2026
Minimax Optimality of the NPMLE for Gaussian Mixtures in Hellinger Distance
We analyze the problem of estimating univariate Gaussian mixture densities using the nonparametric maximum likelihood estimator (NPMLE) based on $n$ independent and identically distributed samples. We show that the unconstrained NPMLE achieves the minimax optimal rate $\log(n)/n$ in squared Hellinger distance, when the...
Shayan Hundrieser, Tudor Manole
· 1 citation