On a new multivariate two-sample test

By Ludwig Baringhaus, C. Franz. 2004

423 citations recorded by the source corpus.

Subfields: Statistics and Probability, Statistical Learning Theory

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Citations in the corpus

Interpretable Distribution Features with Maximum Testing Power (2016, methodology): “…tests based on RKHS distances (Eric et al., 2008; Fromont et al., 2012; Gretton et al., 2012a) or energy distances (Székely and Rizzo, 2004; Baringhaus and Franz, 2004) have as their test statistic an integral probability metric, the Maximum Mean Discrepancy (Gretton et al., 2012a;…”
Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing (2015, background): “A related but different class of tests are distance-based “energy statistics” as introduced in parallel by Baringhaus and Franz [2004] and Sz´ekely and Rizzo [2004], and generalized to some kinds of metrics, denoted ρ , for a related independence testing problem, by Lyons [2013].”
Fast Two-Sample Testing with Analytic Representations of Probability Measures (2015, background): “…distance (sup-norm between cumulative distribution functions); the Maximum Mean Discrepancy (MMD) [8], an RKHS norm of the difference between mean embeddings, and the N -distance (also known as energy distance) [33, 30, 3], which is an MMD-based test for a particular family of kernels [24] .”
A Kernel Test for Three-Variable Interactions (2013, methodology): “When a bounded characteristic kernel is used, the above tests are consistent against all alternatives, and their alternative interpretation is as a generalization [29, 3] of energy distance [30, 31] and distance covariance [2, 32].”
Equivalence of distance-based and RKHS-based statistics in hypothesis testing (2012, methodology): “…proposed by Gretton et al. (2008): we generated uni-variate random variables from the Independent Component Analysis (ICA) benchmark densities of Bach and Jordan (2002); rotated them in the product space by an angle between 0 and π/ 4 to introduce dependence; ﬁlled additional dimensions with…”
B-tests: Low Variance Kernel Two-Sample Tests (2013, methodology): “Kernel test statistics include the maximum mean discrepancy [10, 6] (of which the energy distance is an example [18, 2, 22]), which is the distance between expected features of P and Q in the RKHS; the kernel Fisher discriminant [12], which is the distance between expected feature maps normalized by”
Strictly Proper Scoring Rules, Prediction, and Estimation (2007, background): “…particular, if = Rm and Assumption 1 holds, then inequalities (31) and (32) apply and reduce to 2E‖X − Y‖βα − E‖X − X′‖βα − E‖Y − Y′‖βα ≥ 0 (33) and E‖X − X′‖βα ≤ E‖X + X′‖βα, (34) thereby generalizing results of Buja, Logan, Reeds, and Shepp (1994), Székely (2003), and Baringhaus and Franz (2004).”
Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation (2019, methodology): “, problem (II)) and propose a test for this goodness-of-fit using the rank energy statistic which is based on the usual energy statistic (as in [141], also see [8, 139] for definitions and motivation).”
B-test: A Non-parametric, Low Variance Kernel Two-sample Test (2013, background): “These include the maximum mean discrepancy [9, 6] (of which the energy distance is an example [15, 2, 19]), which is the distance between expected features of P and Q in the RHKS; the kernel Fisher discriminant [11], which is the distance between expected feature maps normalized by the feature space”
Tests for the multivariate k-sample problem based on the empirical characteristic function (2008, background): “Baringhaus and Franz 18 , Szekely and Rizzo 19 , and Klebanov et al .”
Robust multivariate nonparametric tests via projection averaging (2018, methodology): “The energy statistic was introduced by Baringhaus and Franz (2004) and Székely and Rizzo (2004) independently.”
On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests (2015, methodology): “An interesting class of tests are distance-based “energy statistics” as introduced originally by [9], and later by [10].”
A test for the two-sample problem based on empirical characteristic functions (2008, methodology): “As competitors we chose the Kolmogorov–Smirnov test (denoted by KS) and the test in Baringhaus and Franz (2004) (denoted by BF).”
Nonparametric multivariate rank tests and their unbiasedness (2012, methodology): “Tests based on distances between observations were considered by Baringhaus and Franz [2], Friedman and Rafsky [8], Henze [15], Maa et al. [25], Rosenbaum [35] and Schilling [37]; the latter also compared the simulated powers of his test with that of the Kolmogorov–Smirnov two-sample test.”