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 -