An Assumption-Free Exact Test For Fixed-Design Linear Models With Exchangeable Errors
| Autor: | Lei, Lihua, Bickel, Peter J. |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1093/biomet/asaa079 |
| Popis: | We propose the Cyclic Permutation Test (CPT) to test general linear hypotheses for linear models. This test is non-randomized 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 $n / p \ge 1 / \alpha - 1$. 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 non-standard cyclic permutation group under the null hypothesis.The power can be further enhanced by solving a secondary non-linear travelling salesman problem, for which the genetic algorithm can find a reasonably good solution. Extensive simulation studies show that the CPT 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. Furthermore, we provide a selective yet extensive literature review of the century-long efforts on this problem, highlighting the novelty of our test. Comment: Accepted by Biometrika; 46 pages |
| Databáze: | arXiv |
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