BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:David Schrittesser (University of Toronto) DTSTART:20221201T190000Z DTEND:20221201T200000Z DTSTAMP:20260423T052758Z UID:OLS/108 DESCRIPTION:Title: No nstandard analysis and statistical decision theory\nby David Schrittes ser (University of Toronto) as part of Online logic seminar\n\n\nAbstract\ nStatistical decision theory takes inspiration from game theory to provide a basic framework in which one can reason about optimality (or lack there of) of statistical procedures\, such as estimators and tests.\n\nOne prope rty of a statistical procedure is "admissibility": Roughly\, a procedure i s admissible if there is no other procedure which does better under all ci rcumstances ("better" in a sense specified by the decision theoretical fra mework\, i.e.\, with respect to a fixed loss function). This is certainly a necessary condition for optimality.\n\nAdmissibility is notoriously hard to characterize. In particular\, establishing a characterization in Bayes ian terms has been an ongoing pursuit for decades in statistical decision theory. Recently we have found a characterization of admissibility in Baye sian terms\, by using prior probability distributions which can take on in finitesimal values. We are also able to draw connections to classical meth ods establishing admissibility\, such as Blyth's method and Stein's charac terization of admissibility (which does partially characterize admissibili ty\, but only under additional\, technical hypotheses). Finally\, our meth od has applications in concrete problems such as the problem of establishi ng the admissibility of the Graybill-Deal estimator.\n\nThe talk will not presuppose any knowledge on statistics or nonstandard analysis. Everything is joint work with D. Roy and H. Duanmu.\n LOCATION:https://researchseminars.org/talk/OLS/108/ END:VEVENT END:VCALENDAR