Zhu Changbo, Wang Jane-Ling
Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, United States.
Department of Statistics, University of California, Davis, Davis, United States.
J R Stat Soc Series B Stat Methodol. 2023 Apr 3;85(3):705-731. doi: 10.1093/jrsssb/qkad021. eCollection 2023 Jul.
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.
检验两个功能数据样本之间的同质性是一项重要任务。虽然对于密集测量的功能数据来说这是可行的，但我们解释了为什么对于稀疏测量的功能数据具有挑战性，并展示了针对此类数据可以采取的措施。特别是，我们表明在一些温和的约束条件下，基于逐点分布检验边际同质性是可行的，并提出了一种新的双样本统计量，它对密集和稀疏测量的功能数据都适用。所提出的检验统计量基于能量距离构建，并推导了检验统计量到其总体版本的收敛速度以及相关排列检验的一致性。我们的方法在合成数据集和真实数据集上都得到了验证。
