Abstract:
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In this talk, we investigate the commonly used bootstrap percentile method to construct confidence intervals when the mean parameter of an exponential family distribution is subject to inequality constraint. Our attention is focused particularly on quantifying the asymptotic coverage probabilities of the percentile confidence intervals based on bootstrapping maximum likelihood estimators. The challenge to obtain asymptotically meaningful results is addressed from Le Cam's perspective on local contiguous models. We illustrate with reference to important examples including the univariate, two-sample and bivariate exponential family distributions. When the true parameter is on or close to the restriction boundary, we discover that the asymptotic coverage probabilities can always exceed the nominal level in the univariate case; however, they can be, surprisingly, under and over the nominal level in the latter two cases. The results provide theoretical justification and guidance on applying the bootstrap percentile method to the constrained inference problems.
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