Testing homogeneity: the trouble with sparse functional data

• 成果类型: Article
• 署名作者: Zhu, Changbo; Wang, Jane-Ling
• 署名单位: University of Notre Dame; University of California System; University of California Davis
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkad021
• 发表日期: 2023
• 页码: 705-731
• 关键词: one-way anova; 2-sample tests; high dimension; distance; covariance; regression; dependence; FRAMEWORK; inference; EQUALITY

摘要

Testing the homogeneity between two samples of functional data is an important task. While this is feasible for intensely measured functional data, we explain why it is challenging for sparsely measured functional data and show what can be done for such data. In particular, we show that testing the marginal homogeneity based on point-wise distributions is feasible under some mild constraints and propose a new two-sample statistic that works well with both intensively and sparsely measured functional data. The proposed test statistic is formulated upon energy distance, and the convergence rate of the test statistic to its population version is derived along with the consistency of the associated permutation test. The aptness of our method is demonstrated on both synthetic and real data sets.