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math.ST2026
Nonparametric Riemannian Empirical Bayes, and Denoising Measurements on Manifolds
Adam Quinn Jaffe, Leonardo V. Santoro, Bodhisattva Sen
We initiate the study of nonparametric empirical Bayes denoising methods in the setting where both the latent variables and their measurements lie on a compact Riemannian manifold,…
math.ST2025
Wasserstein-Cramér-Rao Theory of Unbiased Estimation
Nicolás García Trillos, Adam Quinn Jaffe, Bodhisattva Sen
The quantity of interest in the classical Cramér-Rao theory of unbiased estimation (e.g., the Cramér-Rao lower bound, its exact attainment for exponential families, and asymptotic…
math.ST2025
Consistency and inconsistency in -means clustering
Moïse Blanchard, Adam Quinn Jaffe, Nikita Zhivotovskiy
A celebrated result of Pollard proves asymptotic consistency for -means clustering when the population distribution has finite variance. In this work, we point out that the popu…