A0175
Title: Testing homogeneity: The trouble with sparse functional data
Authors: Changbo Zhu - University of Notre Dame (United States) [presenting]
Jane-Ling Wang - University of California Davis (United States)
Abstract: Testing the homogeneity between two samples of functional data is an important task. While this is feasible for intensely measured functional data, it is explained why it is challenging for sparsely measured functional data and shows what can be done for such data. In particular, it is shown that testing the marginal homogeneity based on point-wise distributions is feasible under some mild constraints and proposes 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 of sparse functional data. The aptness of the method is demonstrated on both synthetic and real data sets.
