TY - JOUR

T1 - A class of multivariate distribution-free tests of independence based on graphs

AU - Heller, R.

AU - Gorfine, M.

AU - Heller, Y.

PY - 2012/12

Y1 - 2012/12

N2 - A class of distribution-free tests is proposed for the independence of two subsets of response coordinates. The tests are based on the pairwise distances across subjects within each subset of the response. A complete graph is induced by each subset of response coordinates, with the sample points as nodes and the pairwise distances as the edge weights. The proposed test statistic depends only on the rank order of edges in these complete graphs. The response vector may be of any dimensions. In particular, the number of samples may be smaller than the dimensions of the response. The test statistic is shown to have a normal limiting distribution with known expectation and variance under the null hypothesis of independence. The exact distribution free null distribution of the test statistic is given for a sample of size 14, and its Monte-Carlo approximation is considered for larger sample sizes. We demonstrate in simulations that this new class of tests has good power properties for very general alternatives.

AB - A class of distribution-free tests is proposed for the independence of two subsets of response coordinates. The tests are based on the pairwise distances across subjects within each subset of the response. A complete graph is induced by each subset of response coordinates, with the sample points as nodes and the pairwise distances as the edge weights. The proposed test statistic depends only on the rank order of edges in these complete graphs. The response vector may be of any dimensions. In particular, the number of samples may be smaller than the dimensions of the response. The test statistic is shown to have a normal limiting distribution with known expectation and variance under the null hypothesis of independence. The exact distribution free null distribution of the test statistic is given for a sample of size 14, and its Monte-Carlo approximation is considered for larger sample sizes. We demonstrate in simulations that this new class of tests has good power properties for very general alternatives.

KW - High-dimensional response

KW - Independence test

KW - Multivariate association

KW - Random vectors

UR - http://www.scopus.com/inward/record.url?scp=84865536580&partnerID=8YFLogxK

U2 - 10.1016/j.jspi.2012.06.003

DO - 10.1016/j.jspi.2012.06.003

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AN - SCOPUS:84865536580

SN - 0378-3758

VL - 142

SP - 3097

EP - 3106

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - 12

ER -