Bootstrapping in non-regular smooth function models

We study the large sample behavior of the standard bootstrap, the mm-out-of-nn bootstrap, and the oracle bootstrap (Giurcanu and Presnell, 2009) [14] percentile confidence intervals in non-regular smooth function models. We show that the oracle bootstrap percentile confidence intervals are consistent while the standard bootstrap and the mm-out-of-nn bootstrap confidence intervals are inconsistent. Further analysis of coverage probabilities reveals that, for large samples, the iterated oracle bootstrap percentile confidence intervals are more accurate than their non-iterated versions. We also describe the large sample local behavior of the bootstrap confidence intervals for parameter values near the points of inconsistency of the standard bootstrap. In a simulation study, we describe the finite sample local behavior of various bootstrap confidence intervals.