Inference via kernel smoothing of bootstrap P values

Resampling methods such as the bootstrap are routinely used to estimate the finite-sample null distributions of a range of test statistics. We present a simple and tractable way to perform classical hypothesis tests based upon a kernel estimate of the CDF of the bootstrap statistics. This approach has a number of appealing features: (i) it can perform well when the number of bootstraps is extremely small, (ii) it is approximately exact, and (iii) it can yield substantial power gains relative to the conventional approach. The proposed approach is likely to be useful when the statistic being bootstrapped is computationally expensive.