A Kernel Two-Sample Test for Functional Data

Abstract

We propose a nonparametric two-sample test procedure based on Maximum Mean Discrepancy (MMD) for testing the hypothesis that two samples of functions have the same underlying distribution, using kernels defined on function spaces. This construction is motivated by a scaling analysis of the efficiency of MMD-based tests for datasets of increasing dimension. Theoretical properties of kernels on function spaces and their associated MMD are established and employed to ascertain the efficacy of the newly proposed test, as well as to assess the effects of using functional reconstructions based on discretised function samples. The theoretical results are demonstrated over a range of synthetic and real world datasets.

arXiv commentAdded to numerics section

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• PROFIT: Projection-based Test in Longitudinal Functional Data
• Statistical Depth Meets Machine Learning: Kernel Mean Embeddings and Depth in Functional Data Analysis
• Testing distributional equality for functional random variables
• Symmetrisation of a class of two-sample tests by mutually considering depth ranks including functional spaces
• A fast and effective kernel two-sample test for large-scale data