Bootstrapping likelihood-ratio-type tests based on convex M-estimation

Abstract

We consider likelihood-ratio-type statistics for testing restrictions on parameters built from a convex M-estimation criterion. In general, these statistics are not asymptotically pivotal. We propose a general simple nonparametric bootstrap procedure that yields asymptotically valid critical and p-values. The method modifies the bootstrap objective function to mimic what happens under the null hypothesis. A Monte-Carlo study illustrates that our method controls level well and is powerful.