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SUMMARY:Wasserstein-Cramer-Rao Theory of Unbiased Estimation
DTSTART:20260904T151500
DTEND:20260904T164500
DTSTAMP:20260916T162742Z
UID:766a54fa440a26c4f6aaf339d82fd2d8f9073c313600c29e055f4220
CATEGORIES:Conferences - Seminars
DESCRIPTION:Bodhisattva Sen\, Columbia University\nThe quantity of interes
 t in the classical Cramer-Rao theory of unbiased estimation (i.e.\, the Cr
 amer-Rao lower bound\, exact efficiency in exponential families\, and asym
 ptotic efficiency of maximum likelihood estimation) is the variance\, whic
 h represents the instability of an estimator when its value is compared to
  the value for an independently-sampled data set from the same distributio
 n.\nIn this paper we are interested in a quantity which represents the ins
 tability of an estimator when its value is compared to the value for an in
 finitesimal additive perturbation of the original data set\; we refer to t
 his as the "sensitivity" of an estimator. The resulting theory of sensitiv
 ity is based on the Wasserstein geometry in the same way that the classi
 cal theory of variance is based on the Fisher-Rao (equivalently\, Hellinge
 r) geometry\, and this insight allows us to determine a collection of resu
 lts which are analogous to the classical case: a Wasserstein-Cramer-Rao l
 ower bound for the sensitivity of any unbiased estimator\, a characterizat
 ion 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.\nWe use these results to treat man
 y statistical examples\, sometimes revealing new optimality properties for
  existing estimators and other times revealing new estimators.\n\nThis is 
 joint work with Nicolas Garcia Trillos (U Wisconsin) and Adam Jaffe (Colum
 bia) and is based on the paper: https://arxiv.org/pdf/2511.07414.
LOCATION:CM 1 517 https://plan.epfl.ch/?room==CM%201%20517
STATUS:CONFIRMED
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