Functional continuum regression

Zhiyang Zhou

Journal of Multivariate Analysis, 2019, vol. 173, issue C, 328-346

Abstract: Functional principal component regression (PCR) can fail to provide good prediction if the response is highly correlated with some excluded functional principal component(s). This situation is common since the construction of functional principal components never involves the response. Aiming at this shortcoming, we develop functional continuum regression (CR). The framework of functional CR includes, as special cases, both functional PCR and functional partial least squares (PLS). Under certain circumstances, functional CR is more accurate than functional PCR and functional PLS both in estimation and prediction; evidence to this effect is provided through simulations and numerical case studies. Also, we demonstrate the consistency of estimators given by functional CR.

Keywords: Functional linear model; Functional partial least squares; Functional principal component analysis; Functional principal component regression; Scalar-on-function regression (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.jmva.2019.03.006

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