This paper analyzes the ﬁnite-sample and asymptotic properties of several bootstrap and m out of n bootstrap methods for constructing conﬁdence interval (CI) endpoints in models deﬁned by moment inequalities. In particular, we consider using these methods directly to construct CI endpoints. By considering two very simple models, the paper shows that neither the bootstrap nor the m out of n bootstrap is valid in ﬁnite samples or in a uniform asymptotic sense in general when applied directly to construct CI endpoints. In contrast, other results in the literature show that other ways of applying the bootstrap, m out of n bootstrap, and subsampling do lead to uniformly asymptotically valid conﬁdence sets in moment inequality models. Thus, the uniform asymptotic validity of resampling methods in moment inequality models depends on the way in which the resampling methods are employed.
Andrews, Donald W.K. and Han, Sukjin, "Bootstrap for Interval Endpoints Defined by Moment Inequalities" (2008). Cowles Foundation Discussion Papers. 1980.