Principal component estimation of functional logistic regression: discussion of two different approaches

Abstract

Over the last few years many methods have been developed for analyzing functional data with different objectives. The purpose of this paper is to predict a binary response variable in terms of a functional variable whose sample information is given by a set of curves measured without error. In order to solve this problem we formulate a functional logistic regression model and propose its estimation by approximating the sample paths in a finite dimensional space generated by a basis. Then, the problem is reduced to a multiple logistic regression model with highly correlated covariates. In order to reduce dimension and to avoid multicollinearity, two different approaches of functional principal component analysis of the sample paths are proposed. Finally, a simulation study for evaluating the estimating performance of the proposed principal component approaches is developed.

Dynamic relations for sparsely sampled Gaussian processes

“…An extension is the generalized functional linear model (GFLM) (James 2002;Escabias et al 2004;Müller and Stadtmüller 2005), one application of which is the classification of functional data (Müller 2005). In the GFLM, the responses are scalars with general, often discrete distributions, such as binomial or Poisson, while the predictors are functional.…”

PCR and PLS for Clusterwise Regression on Functional Data

“…Moreover, for functional data, the number of principal components could be infinite. Thus, the choice of principal components is a trade-off between stability of the linear model and its predictive power (see also Escabias et al (2004)). A solution to this problem is the PLS approach.…”

Anticipated and Adaptive Prediction in Functional Discriminant Analysis

“…Regularization techniques such as principal component regression (PCR) and partial least squares regression (PLS) have been proposed in Preda and Saporta (2005). An estimating procedure of the functional logistic model is proposed by Escabias et al (2004Escabias et al ( , 2005 with environmental applications. Nonparametric models have been proposed by Ferraty and Vieu (2003), Biau et al (2005) and Preda (2007).…”