HYPOTHESIS TESTING FOR HIGH-DIMENSIONAL MULTINOMIALS: A SELECTIVE REVIEW

• 成果类型: Review
• 署名作者: Balakrishnan, Sivaraman; Wasserman, Larry
• 署名单位: Carnegie Mellon University
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/18-AOAS1155SF
• 发表日期: 2018
• 页码: 727-749
• 关键词: GOODNESS-OF-FIT; log-linear models; DENSITY-ESTIMATION; statistics

摘要

The statistical analysis of discrete data has been the subject of extensive statistical research dating back to the work of Pearson. In this survey we review some recently developed methods for testing hypotheses about high-dimensional multinomials. Traditional tests like the chi(2)-test and the likelihood ratio test can have poor power in the high-dimensional setting. Much of the research in this area has focused on finding tests with asymptotically normal limits and developing (stringent) conditions under which tests have normal limits. We argue that this perspective suffers from a significant deficiency: it can exclude many high-dimensional cases when-despite having non-normal null distributions-carefully designed tests can have high power. Finally, we illustrate that taking a minimax perspective and considering refinements of this perspective can lead naturally to powerful and practical tests.