Improving the Reliability of Bootstrap Condence Intervals

This paper investigates the relation between hypothesis testing and the construction of condence intervals, with particular regard to bootstrap tests. In practice, condence intervals are almost always based on Wald tests, and consequently are not invariant under nonlinear reparametrisations. Bootstrap percentile-t condence intervals are an instance of this. However, the (asymptotically) pivotal functions of data and parameters on which likelihood ratio (LR) and Lagrange multiplier (LM) tests depend can be used to construct parametrisation-invariant condence intervals. We show that, whenever an articial regression can be used to nd the restricted

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