Open Access
VOL. 3 | 2008 Kendall’s tau in high-dimensional genomic parsimony
Pranab K. Sen

Editor(s) Bertrand Clarke, Subhashis Ghosal

Inst. Math. Stat. (IMS) Collect., 2008: 251-266 (2008) DOI: 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.


Published: 1 January 2008
First available in Project Euclid: 28 April 2008

Digital Object Identifier: 10.1214/074921708000000183

Primary: 62G10 , 62G99
Secondary: 62P99

Keywords: Bioinformatics , Chen–Stein theorem , dimensional asymptotics , FDR , Multiple hypotheses testing , nonparametrics , permutational invariance , U-statistics

Rights: Copyright © 2008, Institute of Mathematical Statistics

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