ABSTRACT For linear regression and related models, a permutation inference distribution (PID) is introduced. Like the confidence distribution in the Bayesian/Fiducial/Frequentist inference framework, the PID allows the construction of both confidence intervals and p-values. For two-sample problems and pairwise comparisons in ANOVA models, a fast Fourier transformation method can be used to find the exact PID. In general, however, random permutations are required except for small samples where all permutations can be generated. Simulation studies and real data applications are used to evaluate inferences obtained from the PID. PID methods are close to standard parametric methods when the errors are iid and normal. For skewed and heavy tailed errors, PID methods are superior to bootstrap and standard parametric methods.

中文翻译：

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线性回归和相关模型的排列推理分布

摘要 对于线性回归和相关模型，引入了置换推理分布 (PID)。就像贝叶斯/基准/频率推理框架中的置信分布一样，PID 允许构建置信区间和 p 值。对于 ANOVA 模型中的两个样本问题和成对比较，可以使用快速傅立叶变换方法来找到准确的 PID。然而，一般来说，除了可以生成所有排列的小样本外，都需要随机排列。模拟研究和实际数据应用程序用于评估从 PID 获得的推论。当误差为 iid 和 normal 时，PID 方法接近于标准参数方法。对于偏斜和重尾误差，PID 方法优于 bootstrap 和标准参数方法。