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Tests for the multivariate two‐sample problem based on empirical probability measures
Author(s) -
Kim KangKyun,
Foutz Robert V.
Publication year - 1987
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314860
Subject(s) - multivariate statistics , mathematics , nonparametric statistics , statistics , infimum and supremum , random variate , monte carlo method , statistical hypothesis testing , econometrics , random variable , combinatorics
Abstract Nonparametric tests are proposed for the equality of two unknown p ‐variate distributions. Empirical probability measures are defined from samples from the two distributions and used to construct test statistics as the supremum of the absolute differences between empirical probabilities, the supremum being taken over all possible events. The test statistics are truly multivariate in not requiring the artificial ranking of multivariate observations, and they are distribution‐free in the general p ‐variate case. Asymptotic null distributions are obtained. Powers of the proposed tests and a competitor are examined by Monte Carlo techniques.