A likelihood-based inference for a family of non-regular distributions

Abstract

A likelihood-based approach to inference for a family of non-regular distributions whose support is depend on unknown on parameters is considered. This family can result in the likelihood function being unbounded and so the ML estimators do not have desirable asymptotic properties, and asymptotic confidence intervals and tests based on the likelihood are not established. I will talk about the non-regular problem in inference based on the usual likelihood, and introduce a general theory of inference for such family, established by authors.