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October 2010 Deciding the dimension of effective dimension reduction space for functional and high-dimensional data
Yehua Li, Tailen Hsing
Ann. Statist. 38(5): 3028-3062 (October 2010). DOI: 10.1214/10-AOS816


In this paper, we consider regression models with a Hilbert-space-valued predictor and a scalar response, where the response depends on the predictor only through a finite number of projections. The linear subspace spanned by these projections is called the effective dimension reduction (EDR) space. To determine the dimensionality of the EDR space, we focus on the leading principal component scores of the predictor, and propose two sequential χ2 testing procedures under the assumption that the predictor has an elliptically contoured distribution. We further extend these procedures and introduce a test that simultaneously takes into account a large number of principal component scores. The proposed procedures are supported by theory, validated by simulation studies, and illustrated by a real-data example. Our methods and theory are applicable to functional data and high-dimensional multivariate data.


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Yehua Li. Tailen Hsing. "Deciding the dimension of effective dimension reduction space for functional and high-dimensional data." Ann. Statist. 38 (5) 3028 - 3062, October 2010.


Published: October 2010
First available in Project Euclid: 30 August 2010

zbMATH: 1200.62115
MathSciNet: MR2722463
Digital Object Identifier: 10.1214/10-AOS816

Primary: 62J05
Secondary: 62G20 , 62M20

Keywords: Adaptive Neyman test , Dimension reduction , elliptically contoured distribution , Functional data analysis , principal components

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 5 • October 2010
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