Karl Oskar Ekvall: Uniform inference near boundary and singular information points

Abstract

This talk focuses on new advances, and open problems, in the theory and methods for uniform inference on parameters near the boundary of the parameter set. Recent theory gives, for example, score-based confidence regions with asymptotically correct uniform coverage probability. Related results show uniform inference based on Wald and likelihood ratio statistics is more difficult, and in some cases impossible. The talk also outlines connections between boundary problems and settings with a singular Fisher information. Examples using variance components and mixed models illustrate the general theory and suggest several directions for future research.