Asymptotic and bootstrap tests for subspace dimension

Klaus Nordhausen, Hannu Oja, David E. Tyler

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish (US)
Article number104830
JournalJournal of Multivariate Analysis
StatePublished - Mar 2022

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


  • Independent component analysis
  • Order determination
  • Principal component analysis
  • Sliced inverse regression


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