Testing homogeneity: the trouble with sparse functional data

Author:

Zhu Changbo1ORCID,Wang Jane-Ling2

Affiliation:

1. Department of Applied and Computational Mathematics and Statistics, University of Notre Dame , Notre Dame , United States

2. Department of Statistics, University of California, Davis , Davis , United States

Abstract

Abstract 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.

Funder

NIH

NSF

Publisher

Oxford University Press (OUP)

Subject

Statistics, Probability and Uncertainty,Statistics and Probability

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