Upper and Lower Risks and Minimax Procedures

Abstract : The essential goal of R. A. Fisher's fiducial argument was to make posterior inferences about unknown parameters without resorting to a prior distribution. Over the past decade, there have been two major attempts at developing a statistical theory that would accomplish this convincingly. One of these efforts has been described in a series of publications by Fraser, the other in papers by Dempster. From the early work [4], [11], [12], [13], which was tied to a fiducial viewpoint, both authors developed statistical theories that were distinct from the fiducial argument, yet achieved the goal of non-Bayesian posterior inference [5], [6], [7], [8], [14], [15], [16].