Yury Polyanskiy

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math.ST2026

Function estimation in the empirical Bayes setting

Benjamin Kang, Yury Polyanskiy, Anzo Teh

We study function estimation in the empirical Bayes setting for Poisson and normal means. Specifically, given observations $X_{i} \sim f (\cdot; θ_{i})$ with latent parameters $θ_i\sim π…

math.ST2025

Testing and estimation in orthosymmetric Gaussian sequence model

Zeyu Jia, Yury Polyanskiy

We study the Gaussian sequence model, i.e. $X \sim N (I^¸, I_{\infty})$ , where $I^¸ \in I^ \subset ℓ_{2}$ is assumed to be convex and compact. We show that goodness-of-fit…

math.ST2025

Nonparametric MLE for Gaussian Location Mixtures: Certified Computation and Generic Behavior

Yury Polyanskiy, Mark Sellke

We study the nonparametric maximum likelihood estimator $I ¨ $ for Gaussian location mixtures in one dimension. It has been known since (Lindsay, 1983) that given an $n$ -poin…