| Details: |
Several multivariate generalizations of univariate rank based two-sample
tests have been proposed in the literature. But, most of these
generalizations fail to retain the distribution-free property of the
univariate tests in general multivariate set up. In this talk, we will
propose a multivariate generalization of the univariate run test based on
the idea of shortest Hamiltonian path. Unlike Friedman and Rafsky’s (1979)
multivariate run test based on minimal spanning tree, this proposed test
has the distribution-free property in finite sample situations. While most
of the existing nonparametric two-sample tests perform poorly for high
dimensional data, especially when the training sample size is smaller than
the data dimension, our proposed test can be conveniently used in high
dimension small sample size situations. We investigate the power
properties of the proposed test when the sample size remains fixed and
dimension of the data grows to infinity. Several simulated and real data
sets are also analyzed to evaluate its performance. |