On semiparametric regression in functional data analysis

Abstract

The aim of this paper is to provide a selected advanced review on semiparametric regression which is an emergent promising field of researches in functional data analysis. As a deliberate strategy, we decided to focus our discussion on the single functional index regression (SFIR) model in order to fix the ideas about the stakes linked with infinite dimensional problems and about the methodological challenges that one has to solve when building statistical procedure: one of the most challenging issue being the question of dimensionality effects reduction. This will be the first (and the main) part of this discussion and a complete survey of the literature on SFIR model will be presented. In a second attempt, other semiparametric models (and more generally, other dimension reduction models) will be shortly discussed with the double goal of presenting the state of art and of defining challenging tracks for the future. At the end, we will discuss how additive modeling is an appealing idea for more complicated models involving multifunctional predictors and some tracks for the future will be pointed in this setting. This article is categorized under: Statistical Models > Semiparametric Models Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods

Nonparametric Partial Linear Estimation for Spatial Functional Data with Missing At-Random

“…Other approaches have been proposed to estimate SPFLR model parameters; we cite, for example, the local linear approach used by [14], the robust procedures considered by [15], the k nearest neighbors (kNN) procedure used by [16] and Bayesian approaches proposed by [17]. For recent advances, we can consult the bibliographic reviews in [6,18]. Furthermore, only a few research works have paid attention to estimation in the semi-functional partial linear regression model for spatially dependent observations.…”

A Literature Review of Semi-functional Partial Linear Regression Models

“… Single-index model : The SFPLR with single-index models are: functional partial linear single-index model (FPLSIM) [80], with B-spline approximations [81] , with profile least-squares estimation (PLSE) for slope [82] and Partially Linear Generalized Single Index Models for Functional Data (PLGSIMF) [83]. The systemic review of semiparametric regression (single functional index regression (SFIR)) model is available [84].  Measurement error: There are some extensions that variables have measurement error, such as the model with error-in-response and FPCA estimation [85], non-functional covariate with error, its test and with corrected profile least-squares based estimation [86,87], both scalar and functional covariate measured with additive error [88].…”

Functional Nonparametric Predictions in Food Industry Using Near-Infrared Spectroscopy Measurement

“…Furthermore, using cross-validation and Bayesian techniques, [13,14] proposed and investigated bandwidth selections. Reference [15] suggested a knearest-neighbors (k-NN) approach and obtained the asymptotic performances of k-NN estimators, whereas [16] investigated a semi-functional partly linear regression model with random responses. Reference [17] investigated semi-functional partial linear regression for spatial data and obtained asymptotic normality of the parametric component as well as probability convergence with the rate of the nonparametric component.…”