Permutation Tests at Nonparametric Rates

• 成果类型: Article
• 署名作者: Bertanha, Marinho; Chung, Eunyi
• 署名单位: University of Notre Dame; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2087660
• 发表日期: 2023
• 页码: 2833-2846
• 关键词: confidence-intervals; randomization tests; order-statistics; regression; inference; robust; bootstrap; density

摘要

Classical two-sample permutation tests for equality of distributions have exact size in finite samples, but they fail to control size for testing equality of parameters that summarize each distribution. This article proposes permutation tests for equality of parameters that are estimated at root-n or slower rates. Our general framework applies to both parametric and nonparametric models, with two samples or one sample split into two subsamples. Our tests have correct size asymptotically while preserving exact size in finite samples when distributions are equal. They have no loss in local asymptotic power compared to tests that use asymptotic critical values. We propose confidence sets with correct coverage in large samples that also have exact coverage in finite samples if distributions are equal up to a transformation. We apply our theory to four commonly-used hypothesis tests of nonparametric functions evaluated at a point. Lastly, simulations show good finite sample properties, and two empirical examples illustrate our tests in practice. Supplementary materials for this article are available online.