Extends minimum-distance estimators to Hellinger distance via reverse data processing inequalities, yielding the first near-linear time algorithms for univariate mixtures of log-concave densities and Gaussians with near-optimal sample complexity.
Self-regularizing property of nonparametric maximum likelihood estimator in mixture models.arXiv preprint arXiv:2008.08244,
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Introduces tangential Bayes denoiser for Riemannian Gaussian mixtures on manifolds via spectral Laplace-Beltrami approximation, with nearly Bayes risk in low noise and minimax optimality on the circle.
NP-EBCIs achieve asymptotic exact coverage for individual effects at logarithmic rates and shorten intervals in simulations compared to isolated treatment.
The voting curve from repeated binary predictions is exactly equivalent to a signed voting signature capturing excess latent mass above the majority threshold at binomial variance scales, via signed Hausdorff moments.
NPMLE attains parametric rates for density and posterior mean estimation in bounded-support Gaussian/Poisson mixtures when mixing is finitely discrete, and the LRT is asymptotically tight iff the mixing distribution is finitely discrete.
Empirical Bayes rebiasing learns the bias distribution from paired noisy estimates to produce shorter calibrated intervals than full debiasing while maintaining coverage.
The paper claims empirical Bayes approaches target different inferential objects than full hierarchical posteriors and recommends redeploying modern computation toward the latter, illustrated via the Tweedie formula.
citing papers explorer
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Density estimation for Hellinger via minimum-distance estimators: mixtures of Gaussians, log-concave, and more
Extends minimum-distance estimators to Hellinger distance via reverse data processing inequalities, yielding the first near-linear time algorithms for univariate mixtures of log-concave densities and Gaussians with near-optimal sample complexity.
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Nonparametric Riemannian Empirical Bayes, and Denoising Measurements on Manifolds
Introduces tangential Bayes denoiser for Riemannian Gaussian mixtures on manifolds via spectral Laplace-Beltrami approximation, with nearly Bayes risk in low noise and minimax optimality on the circle.
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Nonparametric Empirical Bayes Confidence Intervals
NP-EBCIs achieve asymptotic exact coverage for individual effects at logarithmic rates and shorten intervals in simulations compared to isolated treatment.
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When Can Voting Help, Hurt, or Change Course? Exact Structure of Binary Test-Time Aggregation
The voting curve from repeated binary predictions is exactly equivalent to a signed voting signature capturing excess latent mass above the majority threshold at binomial variance scales, via signed Hausdorff moments.
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Adaptivity of the NPMLE to finitely discrete mixing distributions in Gaussian/Poisson mixtures
NPMLE attains parametric rates for density and posterior mean estimation in bounded-support Gaussian/Poisson mixtures when mixing is finitely discrete, and the LRT is asymptotically tight iff the mixing distribution is finitely discrete.
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Empirical Bayes Rebiasing
Empirical Bayes rebiasing learns the bias distribution from paired noisy estimates to produce shorter calibrated intervals than full debiasing while maintaining coverage.
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An Old Look at Empirical Bayes
The paper claims empirical Bayes approaches target different inferential objects than full hierarchical posteriors and recommends redeploying modern computation toward the latter, illustrated via the Tweedie formula.