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Abstract:
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In the case of independent identically distributed samples, the naive bootstrap yields confidence limits that are asymptotically correct to the first order, but have less certain confidence coverage in small samples. Bayesian credibility intervals based on the posterior distribution of the model parameters tend to perform better for small samples, but are more dependent on modeling assumptions than the bootstrap. A discrepancy statistic based on the difference of model and bootstrap estimates of standard error is used as a basis for combining bootstrap and Bayesian inferences. The goal is to achieve a compromise that combines the advantages of those two methods, yielding intervals that combine robustness with good small-sample confidence coverage. We assess properties of our method by some simple simulation experiments.
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