Testing homogeneity: the trouble with sparse functional data
本文解释了为什么稀疏函数数据下检验两组样本同质性很困难，并提出一种基于能量距离的检验统计量，适用于密集和稀疏数据，通过模拟和真实数据验证了方法有效性。
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.