Testing homogeneity: the trouble with sparse functional data

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