Two‐stage U‐statistics for Hypothesis Testing

By Hwai-Chung Ho, Grace S. Shieh. 2006

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A Kernelized Stein Discrepancy for Goodness-of-fit Tests (2016, methodology): “Further computation-efﬁciency trade-off between the linear-and U -statistic can be obtained by block-wise averaging; see Ho & Shieh (2006); Zaremba et al. (2013) for details.”
Fast Two-Sample Testing with Analytic Representations of Probability Measures (2015, background): “Remarkably, such a loss of power is not the rule: for instance, when distinguishing signatures of the Higgs boson from background noise [2] (’Higgs dataset’), we observe that a test based on differences in smoothed empirical characteristic functions outperforms the quadratic-time MMD.”
B-tests: Low Variance Kernel Two-Sample Tests (2013, methodology): “Finally, [13] propose an alternative approach for U-statistic based testing when the degree of degeneracy is known: a new U-statistic (the TU-statistic) is written in terms of products of centred U-statistics computed on the individual blocks, and a test is formulated using this TU-statistic.”