An omnibus non-parametric test of equality in distribution for unknown functions

• 成果类型: Article
• 署名作者: Luedtke, Alex; Carone, Marco; van der Laan, Mark J.
• 署名单位: University of Washington; University of Washington Seattle; Fred Hutchinson Cancer Center; University of California System; University of California Berkeley
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12299
• 发表日期: 2019
• 页码: 75-99
• 关键词: STATISTICS; kernel

摘要

We present a novel family of non-parametric omnibus tests of the hypothesis that two unknown but estimable functions are equal in distribution when applied to the observed data structure. We developed these tests, which represent a generalization of the maximum mean discrepancy tests described by Gretton and colleagues, using recent developments from the higher order pathwise differentiability literature. Despite their complex derivation, the associated test statistics can be expressed quite simply as U-statistics. We study the asymptotic behaviour of the proposed tests under the null hypothesis and under both fixed and local alternatives. We provide examples to which our tests can be applied and show that they perform well in a simulation study. As an important special case, our proposed tests can be used to determine whether an unknown function, such as the conditional average treatment effect, is equal to zero almost surely.