Kendall's tau in high-dimensional genomic parsimony

TL;DR

This paper explores the use of Kendall's tau statistic for high-dimensional genomic data analysis, emphasizing dimensional asymptotics over sample size, and assesses the Chen--Stein theorem's applicability with microarray data.

Contribution

It provides a detailed analysis of Kendall's tau in high-dimensional settings and evaluates the Chen--Stein theorem's relevance for genomic data models.

Findings

Kendall's tau is effective in high-dimensional, low-sample-size contexts.

Dimensional asymptotics are more appropriate than sample size asymptotics for this analysis.

Applications demonstrate the method's utility in microarray data models.

Abstract

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.