Using basis expansions for estimating functional PLS regression

Functional regression on remote sensing data in oceanography

“…This method is based on regressing the response on FPLS scores which are obtained from the maximization of the covariance between the functional predictor χ(t) and the scalar response Y . Since FPLS components are more related to the variability of the response, they are more relevant to predicting the outcome (Preda and Saporta, 2005;Aguilera et al, 2010;Febrero-Bande et al, 2015). Similarly to the case of FPCR, FPLS seeks for an orthonormal basis of functions {φ l } l≥1 allowing predictors and the functional parameter to be expanded as χ(t) = µ χ + ∞ l=1 υ l φ l (t) and β(t) = ∞ l=1 c l φ l (t), respectively.…”

“…FLRMs have a wide range of use in various fields such as chemometry, biomechanics and environmental sciences. Particularly, there are many studies that focus on modelling scalar responses on functional predictors (Aguilera et al, 2010;James, 2002;Cardot et al, 1999). A recent review on FLRMs for scalar responses can be found in Reiss et al (2017).…”

Rejoinder on: Probability enhanced effective dimension reduction for classifying sparse functional data

“…The idea of PLS has been seen advantageous over PCA for regression and classification problems in both multivariate and functional data analysis. In particular, Aguilera et al (2010), Hall and Delaigle (2012), Preda and Saporta (2005), Reiss and Ogden (2007), have studied PLS for functional linear regression and classification problems via the approach of estimating the conditional distribution of Y |X . The main problem with FPCA for regression or classification is to ignore the relationship between the predictor and response, which has been also emphasized in the current paper.…”

Functional Data Analysis of Spectroscopic Data with Application to Classification of Colon Polyps

“…In recent years, there have been an increasing number of publications on FDA, including functional linear regression with functional predictors and scalar responses, and its applications in NIR spectroscopy, particularly in the area of biomedical applications [8] [9] [10]. In classification problems, generalized linear model was adapted to the presence of functional predictor variables [11] [12].…”