Multivariate Two-Sample Tests Based on Nearest Neighbors

By M. Schilling. 1986

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Citations in the corpus

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 Two Sample Distribution-Free Test for Functional Data with Application to a Diffusion Tensor Imaging Study of Multiple Sclerosis (2016, background): “One possible approach to test hypothesis (3) is to consider two-sample multivariate procedures; see for example Wei and Lachin (1984), Schilling (1986) or Bohm and Zech (2010), chapter 10.”
TESTING FOR EQUAL DISTRIBUTIONS IN HIGH DIMENSION (2004, methodology): “Schilling (1986) derived the mean and variance of the distribution of T n,2 for selected values of n 1 /n”
Nonparametric multivariate rank tests and their unbiasedness (2012, result): “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.”
An exact distribution‐free test comparing two multivariate distributions based on adjacency (2005, methodology): “Schilling (1986) and Henze (1988) used one or more nearest neighbours of each observation, counting the number of times that the nearest neighbours come from the same group.”
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”
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).”
Fréchet analysis of variance for random objects (2017, background): “Nearest neighbor based tests (Henze, 1988; Henze and Penrose, 1999; Schilling, 1986) count the number of K-nearest neighbor comparisons for which the observations and their neighbors belong to the same sample.”
Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation (2019, unknown): “Various interesting modifications and extensions to this test have been proposed in literature, see, for example, Chen and Friedman (2017), Henze (1988), Schilling (1986), and Petrie (2016).”
New test for the multivariate two-sample problem based on the concept of minimum energy (2003, background): “Since the value of the free parameter k has to be chosen independently from the result and since there is no prescription on how to choose k [20], we did not tabulate its power values for considered distributions.”
Robust multivariate nonparametric tests via projection averaging (2018, methodology): “ energy distance is a special case of the MMD associated with the kernel induced by the Euclidean distance. Another line of work is based on graph constructions including the k-nearest neighbor (NN) (Schilling, 1986;Henze,1988;Mondal et al.,2015) and the minimum spanning tree (Friedman and Rafsky,19”