论文标题
测试同质性：稀疏功能数据的麻烦
Testing Homogeneity: The Trouble with Sparse Functional Data
论文作者
论文摘要
测试两个功能数据样本之间的同质性是一项重要任务。虽然这对于经过详细测量的功能数据是可行的，但我们解释了为什么对于稀疏测量的功能数据而言，它具有挑战性，并说明可以为此类数据做些什么。特别是，我们表明，在某些约束下，基于点分布的边际同质性是可行的，并提出了一个新的两个样本统计量，该统计量与强度和稀疏测量的功能数据都很好。提出的测试统计量是在能量距离时提出的，临界值是通过排列测试获得的。测试统计量的收敛速率与相关置换测试的一致性一起得出。据我们所知，这是第一篇为测试稀疏功能数据测试均匀性的保证一致性的论文。在合成和真实数据集中证明了我们方法的恰当性。
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 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 critical value is obtained via the permutation test. The convergence rate of the test statistic to its population version is derived along with the consistency of the associated permutation test. To the best of our knowledge, this is the first paper that provides guaranteed consistency for testing the homogeneity for sparse functional data. The aptness of our method is demonstrated on both synthetic and real data sets.
