An assumption-free exact test for fixed-design linear models with exchangeable errors

研究问题: 对于任意固定设计矩阵及可交换误差的线性模型，能否构造无需随机化、具有有限样本精确第一类错误率的一般线性假设检验？
方法与思路: 作者通过线性系统构造在原假设下具有循环置换不变性的线性统计量，再作边际秩检验，并以旅行商优化改善功效。
材料陈述的贡献: 摘要称，在显著性水平倒数为整数及相应样本规模条件下，检验具有精确错误率；对单一系数对比还可反演得到精确置信区间。
阅读关注点: 应核对误差可交换性的要求、样本量与参数数的比例条件、循环不变性的构造，以及非线性优化对功效和计算的影响。
阅读边界: 仅据所给 Crossref 摘要；题名中的“无假设”仍以误差可交换性等明确条件为前提。摘要未说明区间形态与全部功效边界，亦未提供其他版本变化。

GPT-6.1 Sol · 高 · 2026-10-03

原文摘要

Summary We propose the cyclic permutation test to test general linear hypotheses for linear models. The test is nonrandomized and valid in finite samples with exact Type I error $\alpha$ for an arbitrary fixed design matrix and arbitrary exchangeable errors, whenever $1 / \alpha$ is an integer and $n / p \geqslant 1 / \alpha - 1$ , where $n$ is the sample size and $p$ is the number of parameters. The test involves applying the marginal rank test to $1 / \alpha$ linear statistics of the outcome vector, where the coefficient vectors are determined by solving a linear system such that the joint distribution of the linear statistics is invariant with respect to a nonstandard cyclic permutation group under the null hypothesis. The power can be further enhanced by solving a secondary nonlinear travelling salesman problem, for which the genetic algorithm can find a reasonably good solution. Extensive simulation studies show that the cyclic permutation test has comparable power to existing tests. When testing for a single contrast of coefficients, an exact confidence interval can be obtained by inverting the test.Summary We propose the cyclic permutation test to test general linear hypotheses for linear models. The test is nonrandomized and valid in finite samples with exact Type I error $\alpha$ for an arbitrary fixed design matrix and arbitrary exchangeable errors, whenever $1 / \alpha$ is an integer and $n / p \geqslant 1 / \alpha - 1$, where $n$ is the sample size and $p$ is the number of parameters. The test involves applying the marginal rank test to $1 / \alpha$ linear statistics of the outcome vector, where the coefficient vectors are determined by solving a linear system such that the joint distribution of the linear statistics is invariant with respect to a nonstandard cyclic permutation group under the null hypothesis. The power can be further enhanced by solving a secondary nonlinear travelling salesman problem, for which the genetic algorithm can find a reasonably good solution. Extensive simulation studies show that the cyclic permutation test has comparable power to existing tests. When testing for a single contrast of coefficients, an exact confidence interval can be obtained by inverting the test.

摘要来源：Crossref

笔记与分组

分类依据与纠错

An assumption-free exact test for fixed-design linear models with exchangeable errors

代码、数据与补充材料

可交换误差下固定设计线性模型的精确检验

原文摘要

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