Empirical Distributions of Beliefs Under Imperfect Observation

Authors:
Olivier Gossner;Tristan Tomala
Affiliations:
Paris-Jourdan Sciences Economiques, UMR CNRS-EHESS-ENS-ENPC 8545, 48 Boulevard Jourdan, 75014 Paris, France, and MEDS, Kellogg School of Management, Northwestern University, Evanston, Illinois 602 ...;CEREMADE, UMR CNRS 7534 Universit Paris-Dauphine, Place de Lattre de Tassigny, 75016 Paris, France
Venue:
Mathematics of Operations Research
Year:
2006

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Abstract

Let (xn)n be a process with values in a finite set X and law P, and let yn f(xn) be a function of the process. At stage n, the conditional distribution pn P(xnx1,,xn1), element of (X), is the belief that a perfect observer, who observes the process online, holds on its realization at stage n. A statistician observing the signals y1,,yn holds a belief enP(pnx1,,xn) () on the possible predictions of the perfect observer. Given X and f, we characterize the set of limits of expected empirical distributions of the process (en) when P ranges over all possible laws of (xn)n.