Asymptotic and bootstrap tests for subspace dimension

JOURNAL OF MULTIVARIATE ANALYSIS

卷:188

Article

Nordhausen, Klaus¹  Oja, Hannu²  Tyler, David E.³ 

[1] Univ Jyvaskyla, Dept Math & Stat, Jyvaskyla, Finland

[2] Univ Turku, Dept Math & Stat, Turku, Finland

[3] State Univ New Jersey, Dept Stat, Piscataway, NJ USA

关键词: Independent component analysis;    Order determination;    Principal component analysis;    Sliced inverse regression;   

DOI  :  10.1016/j.jmva.2021.104830

来源: Elsevier

【 摘 要 】

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. (C) 2021 The Author(s). Published by Elsevier Inc.

【 授权许可】

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