Multivariate generalizations of the Wald--Wolfowitz and Smirnov two-sample tests

By Jerome H. Friedman, Lawrence C. Rafsky. 1979

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Citations in the corpus

On the (Statistical) Detection of Adversarial Examples (2017, neutral): “H 0”
Counterfactual Normalization: Proactively Addressing Dataset Shift and Improving Reliability Using Causal Mechanisms (2018, background): “One measure of separability of classes is based off of a test (Friedman and Rafsky, 1979) for determining if two samples are from the same distribution.”
A Test of Relative Similarity For Model Selection in Generative Models (2015, background): “Other two sample tests are not easily extendable to relative tests (Rosenbaum, 2005; Friedman and Rafsky, 1979; Hall and Tajvidi, 2002).”
Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing (2015, methodology): “…book Lehmann and D’Abrera [2006] and the runs test by Wald and Wolfowitz [1940], while some interesting multivariate tests include spanning tree methods by Friedman and Rafsky [1979], nearest-neighbor based tests by Schilling [1986] and Henze [1988], and the “cross-match” tests by Rosenbaum [2005].”
FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Test (2014, background): “This task, however, is very difficult and challenging in practice since the underneath distribution information are generally unknown apriori (Bickel, 1969; Friedman & Rafsky, 1979; Hall & Tajvidi, 2002; Biau & Gyofi, 2005).”
Testing Hypotheses by Regularized Maximum Mean Discrepancy (2013, methodology): “MMD [9] was experimentally shown to outperform many traditional two-sample tests such as the generalized Wald-Wolfowitz test, the generalized Kolmogorov-Smirnov (KS) test [2], the Hall-Tajvidi (Hall) test [12], and the Biau-Györf test.”
A Kernel Method for the Two-Sample-Problem (2006, methodology): “A generalisation of the Wald-Wolfowitz runs test to the multivariate domain was proposed and analysed in [12, 17] ( Wolf), which involves counting the number of edges in the minimum spanning tree over the aggregated data that connect points inX to points inY .”
Pose-based human action recognition via sparse representation in dissimilarity space (2014, methodology): “The problem of computing a dissimilarity value can be viewed from different perspectives: using dynamic programmin g in order to estimate the non-linea r warping between the two trajectories in the feature space [3], transforming the problem into the graph domain and comparing the correspondi ng gra”
A Kernel Two-Sample Test (2012, methodology): “Two possible generalisations of the Kolmogorov-Smirnov test to the multivariate case were studied by Bickel (1969) and Friedman and Rafsky (1979).”
Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds (2008, methodology): “Another possible connection to multivariate analysis is via the Friedman and Rafsky (1979) test, which employs MSTs of pooled sample points.”
A Fast, Consistent Kernel Two-Sample Test (2009, methodology): “We summarize ou r results in Table 1. Note that an extensive benchmark of the MMD Boot and Pears tests against other nonparametric approaches to two-sample testing is provided in [14]: these include the th e Friedman-Rafsky generalisation of the Kolmogorov-Smirnov and Wald-Wolfowitz tests [ 9 ], the”
A test for the two-sample problem based on empirical characteristic functions (2008, background): “Friedman and Rafsky (1979) have proposed a multivariate generalization of the Wald-Wolfowitz runs test for testing the equality of two density functions, which is asymptotically distribution free under the null hypothesis and consistent against general alternatives (these properties were proved by H”
Robust multivariate nonparametric tests via projection averaging (2018, methodology): “To control the randomness from cα,CvM, we use a similar idea in Fromont et al. (2013) (see also Albert, 2015) where they considered the quantile of a permutation critical value.”