A MULTIVARIATE TWO-SAMPLE TEST BASED ON THE NUMBER OF NEAREST NEIGHBOR TYPE COINCIDENCES

By Norbert Henze. 1988

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

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].”
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.”
On boosting the power of Chatterjee’s rank correlation (2021, background): “…Dette–Siburg–Stoimenov’s correlation measure ξ, and thus intuitively will suffer from similar efficiency loss as other 1-NN-based estimators in various applications (Wald and Wolfowitz, 1940; Friedman and Rafsky, 1979; Henze, 1988; Liu and Singh, 1993; Henze and Penrose, 1999; Bhattacharya, 2019).”
New test for the multivariate two-sample problem based on the concept of minimum energy (2003, methodology): “The extension of the Wald–Wolfowitz run test [7] and the nearest neighbor test [8] avoid these caveats, but it is not obvious that they are sensitive to all kinds of differences in the parent distributions from which the samples are drawn.”
TESTING FOR EQUAL DISTRIBUTIONS IN HIGH DIMENSION (2004, methodology): “Henze (1988) proved that the limiting distribution of a class of nearest neighbor statistics is normal for any distance generated by a norm on R d .”
Robust multivariate nonparametric tests via projection averaging (2018, background): “Hoeffding (1952) established a sufficient condition (indeed the necessary condition proved by Chung and Romano, 2013) under which the permutation distribution approximates the corresponding unconditional distribution.”
Normal Approximation in Geometric Probability (2004, methodology): “This example is relevant to the multivariate two-sample test described by Henze [ 8 ].”
An exact distribution‐free test comparing two multivariate distributions based on adjacency (2005, methodology): “Essentially the quantity p also plays a central role in the limiting behaviour of the FriedmanRafsky runs statistic, and it is a member of the family of measures of distributional separation that was proposed by Gy6rfi and Nemetz; see Henze and Penrose (1999), theorem 2.”
On Azadkia–Chatterjee’s conditional dependence coefficient (2021, background): “…Friedman and Rafsky (1979) extended Wald and Wolfowitz (1940)’s rank-based run test to multivariate spaces via minimum spanning trees; see, also, Henze (1988), Liu and Singh (1993), Henze and Penrose (1999), and Bhattacharya (2019) for other notable results along that track, and Devroye et al.…”
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): “[66] Henze, N.”
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”