On the asymptotic properties of a nonparametric L/sub 1/-test statistic of homogeneity

By Gérard Biau, László Györfi. 2005

52 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “The MMD test has several advantages over existing methods proposed in the literature (Anderson et al. 1994, Biau and Györfi 2005, Nguyen et al. 2007).”
FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Test (2014, methodology): “The core idea of FastMMD is to equivalently transform the MMD with shiftinvariant kernels into the amplitude expectation of a linear combination of sinusoid components based on Bochner’s theorem and Fourier transform (Rahimi & Recht, 2007).”
A Kernel Method for the Two-Sample-Problem (2006, methodology): “L1 or L2) between Parzen window estimates of the densities as a test statistic [1, 3], based on the asymptotic distribution of this distance given p = q.”
Integrating structured biological data by Kernel Maximum Mean Discrepancy (2006, methodology): “Another approach is to use some distance (e.g. L1 or L2) between estimates of the densities as a test statistic (Anderson et al., 1994; Biau and Gyorfi, 2005), based on the asymptotic distribution of this distance given p = q.”
Least-squares two-sample test (2011, methodology): “MMD was experimentally shown to outperform other homogeneity tests such as the generalized Kolmogorov-Smirnov test (Friedman & Rafsky, 1979), the generalized Wald-Wolfowitz test (Friedman & Rafsky, 1979), the Hall-Tajvidi test (Hall & Tajvidi, 2002), and the Biau-Györfi test (Biau & Györfi, 2005).”
Consistent Nonparametric Tests of Independence (2010, background): “Beirlant, Devroye, Györfi, and Vajda (2001), and Biau and Györfi (2005) proved that, for all 0 < ε, P{Ln(μn,1, μ1) > ε} ≤ 2mne−nε 2/2.”
Strongly consistent nonparametric tests of conditional independence (2012, background): “Devroye and Lugosi (2002), Biau and Györfi (2005), and Gretton and Györfi (2010) provide further discussion and references.”
A Kernel Two-Sample Test (2012, background): “Biau and Gyorfi (2005)(Biau) use as their test statistic theL1 distance between discretized estimates of the probabilities, where the partitioning is refined as the sample size increases.”