DECIDING THE DIMENSION OF EFFECTIVE DIMENSION REDUCTION SPACE FOR FUNCTIONAL AND HIGH-DIMENSIONAL DATA
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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 χ 2 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.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/9fbab1b0c160b89108578183a6e0e8e4ed6dfd5a
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In Statistics and Probability
Citations in the corpus
- Partially Linear Functional Additive Models for Multivariate Functional Data (2018, methodology): “The most widely used approach is to project functional data into a low-rank functional subspace and use the projections as predictors in a nonlinear model (James and Silverman 2005; Li and Hsing 2010a; Yao, Lei, and Wu 2015).”