A1 Journal article (refereed)
Asymptotic and bootstrap tests for subspace dimension (2021)

Nordhausen, K., Oja, H., & Tyler, D. E. (2021). Asymptotic and bootstrap tests for subspace dimension. Journal of Multivariate Analysis, In Press. 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: 2021

Volume: In Press

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

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


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

Free keywords: Order determination; Principal component analysis; Sliced inverse regression

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Ministry reporting: No, publication in press

Preliminary JUFO rating: 1

Last updated on 2021-16-09 at 16:15