Abstract Modern problems in statistics often include estimators of high computational complexity and with complicated distributions. Statistical inference on such estimators usually relies on asymptotic normality assumptions, however, such assumptions are often not applicable for available sample sizes, due to dependencies in the data. A common alternative is the use of resampling procedures, such as bootstrapping, but these may be computationally intensive to an extent that renders them impractical for modern problems. In this article, we develop a method for fast construction of test-inversion bootstrap confidence intervals. Our approach uses quantile regression to model the quantile of an estimator conditional on the true value of the parameter. We apply this to the Watterson estimator of mutation rate in a standard coalescent model. We demonstrate an improved efficiency of up to 40% from using quantile regression compared to state of the art methods based on stochastic approximation, as measured by the number of simulations required to achieve comparable accuracy. Supplementary materials for this article are available online.

中文翻译：

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使用分位数回归有效构建测试反演置信区间

摘要 现代统计学问题通常包括计算复杂度高且分布复杂的估计量。对此类估计量的统计推断通常依赖于渐近正态性假设，但是，由于数据中的依赖性，此类假设通常不适用于可用的样本量。一种常见的替代方法是使用重采样程序，例如引导程序，但这些程序可能需要大量计算，以至于无法解决现代问题。在本文中，我们开发了一种快速构建测试反演自举置信区间的方法。我们的方法使用分位数回归来对以参数真实值为条件的估计量的分位数进行建模。我们将其应用于标准聚结模型中突变率的 Watterson 估计量。与基于随机近似的最先进方法相比，我们证明了使用分位数回归的效率提高了 40%，这是通过实现可比精度所需的模拟数量来衡量的。本文的补充材料可在线获取。