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math.ST2026
An Empirical Bayes Perspective on Heteroskedastic Mean Estimation
Yanjun Han, Abhishek Shetty, Jacob Shkrob
Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observatio…
math.ST2025
Approximate independence of permutation mixtures
Yanjun Han, Jonathan Niles-Weed
We prove bounds on statistical distances between high-dimensional exchangeable mixture distributions (which we call \emph{permutation mixtures}) and their i.i.d. counterparts. Our…
math.ST2025
Besting Good--Turing: Optimality of Non-Parametric Maximum Likelihood for Distribution Estimation
Yanjun Han, Jonathan Niles-Weed, Yandi Shen +1
When faced with a small sample from a large universe of possible outcomes, scientists often turn to the venerable Good--Turing estimator. Despite its pedigree, however, this estima…