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 to have made a resurgence recently under various names and modifications.
For example under the new name 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 angle.
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 posses good repeated sampling, frequentist properties. As an example we apply the recipe to interval observed mixed linear model.
Portions of this talk are based on a joined work with Hari Iyer, Thomas C.M. Lee and Jessi Cisewski
Jan Hannig is an Associate Professor in the Department of Statistics and Operations Research at the University of North Carolina at Chapel Hill. His current research interests are: applied probability, theoretical statistics, generalized fiducial inference and applications to biology and engineering.
Jan Hannig received his Mgr (MS equivalent) in mathematics in 1996 from the Charles University, Prague, Czech Republic. He received his Ph.D. in statistics and probability in 2000 from Michigan State University under the direction of Professor A.V. Skorokhod. From 2000 to 2008 he was on faculty of the Department of Statistics at Colorado State University where he was promoted to an Associate Professor in 2006. Jan Hannig has been a PI and co-PI on several federally founded projects. To date he has published 38 peer reviewed publications.