Standard confidence intervals employed in applied statistical analysis are usually based on asymptotic approximations. Such approximations can be considerably inaccurate in small and moderate sized samples. We derive accurate confidence intervals based on higher-order approximate quantiles of the score function. The coverage approximation error is $O(n^{-3/2})$ while the approximation error of confidence intervals based on the asymptotic normality of MLEs is $O(n^{-1/2})$. Monte Carlo simulations confirm the theoretical findings. An implementation for regression models and real data applications are provided.

中文翻译：

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高阶近似置信区间

应用统计分析中采用的标准置信区间通常基于渐近近似。在小型和中等规模的样本中，这种近似可能相当不准确。我们根据评分函数的高阶近似分位数推导出准确的置信区间。覆盖近似误差为$O(n^{-3/2})$，而基于MLE 渐近正态性的置信区间的近似误差为$O(n^{-1/2})$。蒙特卡罗模拟证实了理论发现。提供了回归模型和真实数据应用程序的实现。