Statistics Seminar: STA 290
Thursday, October 11th, 2012 at 4.10pm, MSB 1147 (Colloquium Room)
Refreshments 3:30pm, prior to seminar in MSB 4110 (Statistics Lounge)
Speaker: Jan Hannig (University of North Carolina, Chapel Hill)
Title: On generalized fiducial inference
Abstract: R. A. Fisher's fiducial inference has been the subject of many discussions and controversies ever since he introduced the idea during the 1930's. The idea experienced a bumpy ride, to say the least, during its early years and one can safely say that it eventually fell into disfavor among mainstream statisticians. However, it appears the both the interest in, and the practical use of, fiducial inference have experienced a resurgence in recent years under various names and modifications. For example, under the new name of “generalized inference”, fiducial inference has proved to be a useful tool for deriving statistical procedures for problems where frequentist methods with good properties were previously unavailable. Therefore, we believe that the fiducial argument of R.A. Fisher deserves a fresh look from a new perspective.
In this talk, we first generalize Fisher's fiducial argument and obtain a fiducial recipe applicable in virtually any situation. We demonstrate this fiducial recipe on examples of varying complexity. We also investigate, by simulation and by theoretical considerations, some properties of the statistical procedures derived by the fiducial recipe showing they often possess good frequentist properties. We discuss an example in which this recipe is applied to an interval- observed mixed linear model.
Portions of this talk are based on joint work with Hari Iyer, Thomas Lee and Jessi Cisewski.