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 editors: Nordhausen, Klaus; Oja, Hannu; Tyler, David E.
Journal or series: Journal of Multivariate Analysis
ISSN: 0047-259X
eISSN: 1095-7243
Publication year: 2022
Volume: 188
Article number: 104830
Publisher: Elsevier
Publication country: United States
Publication language: English
DOI: https://doi.org/10.1016/j.jmva.2021.104830
Publication open access: Openly available
Publication channel open access: Partially 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.
Keywords: multivariable methods; independent component analysis; estimating (statistical methods)
Free keywords: Order determination; Principal component analysis; Sliced inverse regression
Contributing organizations
Ministry reporting: Yes
Reporting Year: 2022
Preliminary JUFO rating: 1
