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High-order Coverage of Smoothed Bayesian Bootstrap Intervals for Population Quantiles

Authors

  • David M. Kaplan University of Missouri
  • Lonnie Hofmann

Abstract

We characterize the high-order coverage accuracy of smoothed and unsmoothed Bayesian bootstrap confidence intervals for population quantiles. Although the original (Rubin 1981) unsmoothed intervals have the same O(n−1/2) coverage error as the standard empirical bootstrap, the smoothed Bayesian bootstrap of Banks (1988) has much smaller O(n−3/2[log(n)]3) coverage error and is exact in special cases, without requiring any smoothing parameter. It automatically removes an error term of order 1/n that other approaches need to explicitly correct for. This motivates further study of the smoothed Bayesian bootstrap in more complex settings and models.

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How to Cite

Kaplan, D., & Hofmann, L. High-order Coverage of Smoothed Bayesian Bootstrap Intervals for Population Quantiles. Austrian Journal of Statistics, 52(2), 22–44. Retrieved from https://ajs.or.at/index.php/ajs/article/view/1385