  The asymptotic behaviour of the commonly used bootstrap percentile confidence
interval is investigated when the parameters are subject to linear inequality
constraints. We concentrate on the important one- and two-sample problems with
data generated from general parametric distributions in the natural exponential
family. The focus of this paper is on quantifying the coverage probabilities of
the parametric bootstrap percentile confidence intervals, in particular their
limiting behaviour near boundaries. We propose a local asymptotic framework to
study this subtle coverage behaviour. Under this framework, we discover that
when the true parameters are on, or close to, the restriction boundary, the
asymptotic coverage probabilities can always exceed the nominal level in the
one-sample case; however, they can be, remarkably, both under and over the
nominal level in the two-sample case. Using illustrative examples, we show that
the results provide theoretical justification and guidance on applying the
bootstrap percentile method to constrained inference problems.
