NPMLE
Nonparametric Maximum Likelihood Estimation, a statistical method that estimates an unknown distribution or density by maximizing the empirical likelihood over an infinite-dimensional function space. It is commonly used for nonparametric problems such as Gaussian mixture models.
Timeline (last 90 days)
The paper proves that when the true mixture measure satisfies the sub-Gaussian assumption, the unconstrained NPMLE achieves the minimax optimal rate log(n)/n under squared Hellinger distance.
The paper establishes the regret optimality of an NPMLE-based g-modeling procedure in Gaussian empirical Bayes problems with bounded priors.
g-modeling estimates the marginal density f(x) = ∫ φ(x-θ) dG(θ) via the NPMLE, and then obtains an estimate of the prior G through deconvolution.
All Facts (3)
The paper proves that when the true mixture measure satisfies the sub-Gaussian assumption, the unconstrained NPMLE achieves the minimax optimal rate log(n)/n under squared Hellinger distance.
50%UnverifiedThe paper establishes the regret optimality of an NPMLE-based g-modeling procedure in Gaussian empirical Bayes problems with bounded priors.
50%Unverifiedg-modeling estimates the marginal density f(x) = ∫ φ(x-θ) dG(θ) via the NPMLE, and then obtains an estimate of the prior G through deconvolution.
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