Colloquium - Nicolas Trillos - October 30, 2025

Speaker: Nicolas Trillos, University of Wisconsin - Madison
Date/Time: Thursday, October 30, 2025, 10:00 AM - 11:00 AM ET

Title: Wasserstein-Cramér-Rao Theory of Unbiased Estimation

Abstract: The quantity of interest in the classical Cramér-Rao theory of unbiased estimation (i.e., the Cramér- Rao lower bound, exact efficiency in exponential families, and asymptotic efficiency of maximum likelihood estimation) is the variance, which represents the instability of an estimator when its value is compared to the value for an independently sampled data set from the same distribution. In this talk, we will be interested in a quantity that represents the instability of an estimator when its value is compared to the value for an infinitesimal additive perturbation of the original data set; we refer to this as the “sensitivity” of an estimator. The resulting theory of sensitivity is based on the Wasserstein geometry in the same way that the classical theory of variance is based on the Fisher-Rao (equivalently, Hellinger) geometry. I'll present a collection of results which are analogous to the classical case: a Wasserstein-Cramér-Rao lower bound for the sensitivity of any unbiased estimator, a characterization of models in which there exist unbiased estimators achieving the lower bound exactly, and a guarantee that Wasserstein projection estimators achieve the lower bound asymptotically. I'll discuss some simple statistical examples to illustrate the theory, sometimes revealing new optimality properties for existing estimators and other times revealing entirely new ones.  I'll also discuss some of the many open questions that this work (and in fact the whole perspective this work is based on) motivates.

This talk is based on joint work with Adam Quinn Jaffe (Columbia) and Bodhisattva Sen (Columbia). 

Bio: Nicolás García Trillos is an Associate Professor in the Department of Statistics at the University of Wisconsin Madison. From 2015 - 2018, he was a Prager Assistant Professor (postdoctoral position) at Brown University. He finished his Ph.D in mathematics at Carnegie Mellon University in 2015. His research lies at the intersection of applied analysis, statistics, applied probability, and machine learning.

Website: https://www.nicolasgarciat.com/