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

• 成果类型: Article
• 署名作者: Lei, Lihua; Bickel, Peter J.
• 署名单位: Stanford University; University of California System; University of California Berkeley
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asaa079
• 发表日期: 2021
• 页码: 397412
• 关键词: regression; asymptotics

摘要

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 a for an arbitrary fixed design matrix and arbitrary exchangeable errors, whenever 1/alpha is an integer and n/p >= 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.