A1 Journal article (refereed)
Asymptotic and bootstrap tests for subspace dimension (2022)


Nordhausen, K., Oja, H., & Tyler, D. E. (2022). Asymptotic and bootstrap tests for subspace dimension. Journal of Multivariate Analysis, 188, Article 104830. https://doi.org/10.1016/j.jmva.2021.104830


JYU authors or editors


Publication details

All authors or editorsNordhausen, Klaus; Oja, Hannu; Tyler, David E.

Journal or seriesJournal of Multivariate Analysis

ISSN0047-259X

eISSN1095-7243

Publication year2022

Volume188

Article number104830

PublisherElsevier

Publication countryUnited States

Publication languageEnglish

DOIhttps://doi.org/10.1016/j.jmva.2021.104830

Publication open accessOpenly available

Publication channel open accessPartially open access channel

Publication is parallel published (JYX)https://jyx.jyu.fi/handle/123456789/79046

Web address of parallel published publication (pre-print)https://arxiv.org/abs/1611.04908v2


Abstract

Many linear dimension reduction methods proposed in the literature can be formulated using an appropriate pair of scatter matrices. The eigen-decomposition of one scatter matrix with respect to another is then often used to determine the dimension of the signal subspace and to separate signal and noise parts of the data. Three popular dimension reduction methods, namely principal component analysis (PCA), fourth order blind identification (FOBI) and sliced inverse regression (SIR) are considered in detail and the first two moments of subsets of the eigenvalues are used to test for the dimension of the signal space. The limiting null distributions of the test statistics are discussed and novel bootstrap strategies are suggested for the small sample cases. In all three cases, consistent test-based estimates of the signal subspace dimension are introduced as well. The asymptotic and bootstrap tests are illustrated in real data examples.


Keywordsmultivariable methodsindependent component analysisestimating (statistical methods)

Free keywordsOrder determination; Principal component analysis; Sliced inverse regression


Contributing organizations


Ministry reportingYes

Reporting Year2022

JUFO rating1


Last updated on 2024-26-03 at 20:56