Testing the mean and variance by e-processes

• 成果类型: Article
• 署名作者: Fan, Yixuan; Jiao, Zhanyi; Wang, Ruodu
• 署名单位: Tianjin University; Illinois State University; University of Waterloo
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asae049
• 发表日期: 2024
• 关键词: false discovery rate; Value-at-risk; time-uniform; strategy; bounds

摘要

We address the problem of testing the conditional mean and conditional variance for nonstationary data. We build e-values and p-values for four types of nonparametric composite hypothesis with specified mean and variance as well as other conditions on the shape of the data-generating distribution. These shape conditions include symmetry, unimodality and their combination. Using the obtained e-values and p-values, we construct tests via e-processes, also known as testing by betting, as well as some tests based on combining p-values for comparison. Although we mainly focus on one-sided tests, the two-sided test for the mean is also studied. Simulation and empirical studies are conducted under a few settings, and they illustrate features of the methods based on e-processes.