An exact distribution‐free test comparing two multivariate distributions based on adjacency

By Paul R. Rosenbaum. 2005

322 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

On the (Statistical) Detection of Adversarial Examples (2017, background): “lingsT2 test evaluates whether two distributions have the same mean [16]. Several other tests depending on graph or tree properties of the data were proposed by Friedman et al. [10], Rosenbaum et al. [31] or Hall et al. [15]. Most of these tests are not appropriate when considering data with high di”
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].”
A Kernel Method for the Two-Sample-Problem (2006, methodology): “A more recent multivariate test was proposed in [20], which is based on the minimum distance non-bipartite matching over the aggregate data, at cost O((m + n)(3)).”
On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests (2015, unknown): “Some examples of tests quite different from the ones studied here include rank based tests as covered by the excellent book [13], and graphical tests that include spanning tree methods by [14] (generalizing the runs test by [15]), nearest-neighbor based tests by [16,17], and the cross-match tests by”
Principal Differences Analysis: Interpretable Characterization of Differences between Distributions (2015, background): “Unfortunately, this simplicity vanishes as the dimensionality d grows, and complex test-statistics have been designed to address some of the difficulties that appear in high-dimensional settings [5, 6, 7, 8].”
Classification Accuracy as a Proxy for Two Sample Testing (2016, background): “Another class of two-sample tests is based on geometric graphs; examples include the k-nearest neighbor (NN) graph (Schilling, 1986; Henze, 1988), the minimum spanning tree (Friedman and Rafsky, 1979) and the crossmatching (Rosenbaum, 2005).”
On the High-dimensional Power of Linear-time Kernel Two-Sample Testing under Mean-difference Alternatives (2014, background): “pendence testing) in high dimensions in Szekely & Rizzo (2013), but no analysis of power is available or easily derivable. There also exist many other tests under GA like the cross-match test by Rosenbaum (2005), but none of them have been analyzed under HD. 2 Power of MMD l (xed dimension) Let ”
Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation (2019, methodology): “In [128], Rosenbaum constructed his proposed test statistic from a minimum non-bipartite matching (see [90]) of the pooled sample of observations.”
Fréchet analysis of variance for random objects (2017, unknown): “…have been based on nearest neighbors (Henze, 1988; Henze & Penrose, 1999; Schilling, 1986), graphs (Friedman & Rafsky, 1979; Chen & Friedman, 2017; Rosenbaum, 2005), energy statistics (Székely & Rizzo, 2004;50 Lyons, 2013; Székely & Rizzo, 2017) and related work (Baringhaus & Franz, 2004), as…”
Evaluation of subset matching methods and forms of covariate balance (2016, methodology): “Furthermore, to evaluate balance of the joint distributions, we also calculated the standardized cross-match statistic [38].”
Inference for empirical Wasserstein distances on finite spaces (2016, methodology): “comparing the empirical Wasserstein distance W1 after binning on a regular 10×10 grid with the limiting distribution from Theorem 1; 2) a permutation test; 3) the crossmatch test proposed by (Rosenbaum, 2005) and 4) the kernel based test (Anderson et al.”
Nonparametric multivariate rank tests and their unbiasedness (2012, background): “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.”
A Kernel Two-Sample Test (2012, methodology): “A more recent multivariate test was introduced by Rosenbaum (2005).”
On the High Dimensional Power of a Linear-Time Two Sample Test under Mean-shift Alternatives (2015, background): “There also exist many other tests under GA like the cross-match test by Rosenbaum (2005), but none of them have been analyzed under HD. 2 Power of MMDl (fixed dimension) Let us first review the basic argument from Gretton et al. (2012) showing the power in the fixed dimensional setting.”
Robust multivariate nonparametric tests via projection averaging (2018, methodology): “Along with the energy, MMD, NN, FR and BG tests described before, we consider the cross-match test (Rosenbaum, 2005), the multivariate run test (Biswas et al.”
A Survey of Methods for Time Series Change Point Detection (2016, unknown): “This graph can be defined based on a minimum spanning tree [26], minimum distance pairing [52], nearest neighbor graph [26,52], or visibility graph [40,66].”