The Size Distortion of Bootstrap Tests
by
Russell Davidson
Abstract
We provide a theoretical framework in which to study the accuracy of bootstrap
P values, which may be based on a parametric or nonparametric bootstrap. In
the parametric case, the accuracy of a bootstrap test will depend on the shape of
what we call the critical value function. We show that, in many circumstances,
the error in rejection probability of a bootstrap test will be one whole order of
magnitude smaller than that of the corresponding asymptotic test. We also propose
a simulation method for estimating this error that requires the calculation of
only two test statistics per replication
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