Kendall's tau in high-dimensional genomic parsimony

Details Kendall's tau in high-dimensional genomic parsimony Kendall's tau in high-dimensional genomic parsimony

2008-05-21

arxiv.org/abs/0805.3273v1

IMS Collections 2008, Vol. 3, 251-266

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/074921708000000183 the IMS Collections (http://www.imstat.org/publications/imscollec

Scientific paper

10.1214/074921708000000183

High-dimensional data models, often with low sample size, abound in many interdisciplinary studies, genomics and large biological systems being most noteworthy. The conventional assumption of multinormality or linearity of regression may not be plausible for such models which are likely to be statistically complex due to a large number of parameters as well as various underlying restraints. As such, parametric approaches may not be very effective. Anything beyond parametrics, albeit, having increased scope and robustness perspectives, may generally be baffled by the low sample size and hence unable to give reasonable margins of errors. Kendall's tau statistic is exploited in this context with emphasis on dimensional rather than sample size asymptotics. The Chen--Stein theorem has been thoroughly appraised in this study. Applications of these findings in some microarray data models are illustrated.

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