Regularised Manova for High-Dimensional Data

Insha Ullah*, Beatrix Jones

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

The traditional and readily available multivariate analysis of variance (MANOVA) tests such as Wilks' Lambda and the Pillai-Bartlett trace start to suffer from low power as the number of variables approaches the sample size. Moreover, when the number of variables exceeds the number of available observations, these statistics are not available for use. Ridge regularisation of the covariance matrix has been proposed to allow the use of MANOVA in high-dimensional situations and to increase its power when the sample size approaches the number of variables. In this paper two forms of ridge regression are compared to each other and to a novel approach based on lasso regularisation, as well as to more traditional approaches based on principal components and the Moore-Penrose generalised inverse. The performance of the different methods is explored via an extensive simulation study. All the regularised methods perform well; the best method varies across the different scenarios, with margins of victory being relatively modest. We examine a data set of soil compaction profiles at various positions relative to a ridgetop, and illustrate how our results can be used to inform the selection of a regularisation method.

Original languageEnglish
Pages (from-to)377-389
Number of pages13
JournalAustralian and New Zealand Journal of Statistics
Volume57
Issue number3
DOIs
Publication statusPublished - 6 Aug 2015
Externally publishedYes

Fingerprint

Dive into the research topics of 'Regularised Manova for High-Dimensional Data'. Together they form a unique fingerprint.

Cite this