Set Estimation in Locally Identifiable Mixture Models

• Activity Number: 118
• Type: Topic Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Daeyoung Kim*+ and Bruce George Lindsay
• Companies: University of Massachusetts at Amherst and Penn State University
• Keywords: Confidence set ; Finite mixture model ; Identifiability ; Likelihood

Abstract

Statistical inference for the parameters in a parametric model can be done by the method of maximum likelihood which provides procedures for point estimation, set estimation and hypothesis testing. In the set estimation problem there are several literatures that suggest superiority of the likelihood confidence sets over the Wald confidence sets. It is practically important to develop guidance to assess the adequacy of using the Wald confidence sets for the parameters and Fisher information matrix for the ML estimator. In this talk we propose two diagnostics designed to assess difference between the likelihood set and the Wald set for the parameters in any parametric model, and show how one can adapt them to a finite mixture model where the topology of the mixture likelihood is complicated. These diagnostics are based on a set of samples simulated from the modal simulation (Kim and Lindsay, 2011) that efficiently reconstructs the boundaries of the targeted likelihood confidence sets.