Simultaneous likelihood-based bootstrap confidence sets for misspecified models

We consider a multiplier bootstrap procedure for construction of likelihood-based confidence sets for finite samples and a possible model misspecification. The approach is also generalized for the case of simultaneous confidence sets, when the number of parametric models is allowed to be exponentially large w.r.t. the sample size. Theoretical results justify the bootstrap consistency for a fixed sample size. Convincing numerical performance of the bootstrap procedure is demonstrated with experiments for misspecified regression models. This is a joint work with Vladimir Spokoiny.