Asymptotic and bootstrap tests for subspace dimension
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
Published inJournal of Multivariate Analysis
© 2021 the Authors
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.
Publication in research information system
MetadataShow full item record
Additional information about fundingDavid E. Tyler’s research was partially supported by the National Science FoundationGrant No. DMS-1407751.
Showing items with similar title or keywords.
Snowball ICA : A Model Order Free Independent Component Analysis Strategy for Functional Magnetic Resonance Imaging Data Hu, Guoqiang; Waters, Abigail B.; Aslan, Serdar; Frederick, Blaise; Cong, Fengyu; Nickerson, Lisa D. (Frontiers Media, 2020)In independent component analysis (ICA), the selection of model order (i.e., number of components to be extracted) has crucial effects on functional magnetic resonance imaging (fMRI) brain network analysis. Model order ...
Examining stability of independent component analysis based on coefficient and component matrices for voxel-based morphometry of structural magnetic resonance imaging Zhang, Qing; Hu, Guoqiang; Tian, Lili; Ristaniemi, Tapani; Wang, Huili; Chen, Hongjun; Wu, Jianlin; Cong, Fengyu (Springer Netherlands, 2018)Independent component analysis (ICA) on group-level voxel-based morphometry (VBM) produces the coefficient matrix and the component matrix. The former contains variability among multiple subjects for further statistical ...
Nordhausen, Klaus; Ruiz-Gazen, Anne (Elsevier, 2022)Scatter matrices generalize the covariance matrix and are useful in many multivariate data analysis methods, including well-known principal component analysis (PCA), which is based on the diagonalization of the covariance ...
Koesner, Christoph L.; Nordhausen, Klaus (CRAN - The Comprehensive R Archive Network, 2021)The kernel independent component analysis (kernel ICA) method introduced by Bach and Jordan (2003) . The incomplete Cholesky decomposition used in kernel ICA is provided as separate function.
Miettinen, Jari; Matilainen, Markus; Nordhausen, Klaus; Taskinen, Sara (Wiley-Blackwell, 2020)In the independent component model, the multivariate data are assumed to be a mixture of mutually independent latent components. The independent component analysis (ICA) then aims at estimating these latent components. In ...