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Two‐sample homogeneity testing: A procedure based on comparing distributions of interpoint distances
Author(s) -
MonteroManso Pablo,
Vilar José A.
Publication year - 2019
Publication title -
statistical analysis and data mining: the asa data science journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.381
H-Index - 33
eISSN - 1932-1872
pISSN - 1932-1864
DOI - 10.1002/sam.11417
Subject(s) - mathematics , statistic , test statistic , statistics , homogeneity (statistics) , consistency (knowledge bases) , univariate , pairwise comparison , permutation (music) , sample size determination , sample (material) , multivariate statistics , statistical hypothesis testing , discrete mathematics , physics , chemistry , chromatography , acoustics
A new test statistic using interpoint distances is proposed to address the two‐sample problem for multivariate populations. The test statistic compares univariate distributions of within and between samples pairwise distances using a Cramér‐von Mises‐type statistic. The critical values are approximated by means of a permutation procedure and the regularity conditions required to ensure the consistency of the test are established. Unlike other two‐sample procedures, our approach compares the whole distributions of interpoint distances instead of just a few moments, thus obtaining a higher capability to detect differences in their shape or in other moments. An extensive simulation study and experiments with real data sets considered in related papers show a satisfactory performance of the proposed test under a range of alternative distributions. Compared to other two‐sample tests based on interpoint distances, the experiments reveal a more robust behavior in a high‐dimensional setting, being one of the most powerful tests under both location and scales changes.