OPTIMAL NONPARAMETRIC TESTING OF MISSING COMPLETELY AT RANDOM AND ITS CONNECTIONS TO COMPATIBILITY

• 成果类型: Article
• 署名作者: Berrett, Thomas b.; Samworth, Richard j.
• 署名单位: University of Warwick; University of Cambridge
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2326
• 发表日期: 2023
• 页码: 2170-2193
• 关键词: geometry; THEOREMS

摘要

Given a set of incomplete observations, we study the nonparametric problem of testing whether data are Missing Completely At Random (MCAR). Our first contribution is to characterise precisely the set of alternatives that can be distinguished from the MCAR null hypothesis. This reveals interesting and novel links to the theory of Frechet classes (in particular, compatible distributions) and linear programming, that allow us to propose MCAR tests that are consistent against all detectable alternatives. We define an incompatibility index as a natural measure of ease of detectability, establish its key properties and show how it can be computed exactly in some cases and bounded in others. Moreover, we prove that our tests can attain the minimax separation rate according to this measure, up to logarithmic factors. Our methodology does not require any complete cases to be effective, and is available in the R package MCARtest.