A partitioned Single Functional Index Model

Abstract

Given a functional regression model with scalar response, the aim is to present a methodology in order to approximate in a semi-parametric way the unknown regression operator through a single index approach, but taking possible structural changes into account. Our paper presents this methodology and illustrates its behaviour both on simulated and real curves datasets. It appears, from an example of interest in spectrometry, that the method provides a nice exploratory tool both for analyzing structural changes in the spectrum and for visualizing the most informative directions, still keeping good predictive power. Even if the main objective of this work is to discuss applied issues of the method, asymptotic behaviour is shortly described.

Weak convergence of discretely observed functional data with applications

“…Other applications include the functional extensions of regression analysis (for background information see Ramsay and Silverman (2005), Ferraty and Vieu (2006) and Goia and Vieu (2014)), or various statistical testing problems for functional data. Adaptation of the present theory to these settings is, however, not always straightforward, and is part of future research in functional data analysis.…”

Robust estimation for varying index coefficient models

“…In the recent years, the functional data analysis (FDA) has been intensively discussed by many authors. See Goia and Vieu (2014) studied a functional regression model with scalar response. Peng et al (2015) considered the problem of functional parameter estimation for varying coefficient partially functional linear regression models.…”

Editorial to the special issue on Applicable semiparametrics of computational statistics

“…The proposed model is flexible in the nonparametric component which gives good predictive properties, the linearity allows for interpretation and the simplicity of the model allows for ease in practical applications. Using functional regression models with scalar response, in the next paper of this issue, Goia and Vieu (2015) develop a methodology for approximation of the unknown regression operator in a semiparametric manner. Hereby, they propose to use a single index approach that can also take into account potential structural changes.…”