Prof. Ryan Martin : Plausibility functions and exact frequentist inference

Posted by , part of the Statistics and Data Science Seminar.

At

Sept. 5, 2012, 4 p.m.

In

SEO 636

Abstract

In the frequentist program, inferential methods with exact control on error rates are a primary focus. Methods based on asymptotic distribution theory may not be suitable in a particular problem, in which case, a numerical method is needed. In this talk I shall present a general, yet simple, Monte Carlo-driven framework for the construction of frequentist procedures based on plausibility functions. It is proved that the suitably defined plausibility function-based tests and confidence regions have desired frequentist properties. Moreover, in an important special case involving likelihood ratios, conditions are given such that the plausibility function behaves asymptotically like a consistent Bayesian posterior distribution. An extension of the proposed method is also given for the case where nuisance parameters are present. I shall give several examples to illustrate the method's flexibility and to demonstrate its performance compared to existing numerical and analytical methods.