Journal ArticleDOI
Functional quasi-likelihood regression models with smooth random effects
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TLDR
In this paper, a class of semiparametric functional regression models is proposed to describe the influence of vector-valued covariates on a sample of response curves, where each observed curve is viewed as the realization of a random process, composed of an overall mean function and random components.Abstract:
Summary. We propose a class of semiparametric functional regression models to describe the influence of vector-valued covariates on a sample of response curves. Each observed curve is viewed as the realization of a random process, composed of an overall mean function and random components. The finite dimensional covariates influence the random components of the eigenfunction expansion through single-index models that include unknown smooth link and variance functions. The parametric components of the single-index models are estimated via quasi-score estimating equations with link and variance functions being estimated nonparametrically. We obtain several basic asymptotic results. The functional regression models proposed are illustrated with the analysis of a data set consisting of egg laying curves for 1000 female Mediterranean fruit-flies (medflies).read more
Citations
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Functional Data Analysis
TL;DR: In this article, the authors provide an overview of FDA, starting with simple statistical notions such as mean and covariance functions, then covering some core techniques, the most popular of which is functional principal component analysis (FPCA).
Journal ArticleDOI
Functional linear regression analysis for longitudinal data
TL;DR: In this article, a functional linear regression (FLR) method is proposed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time.
Journal ArticleDOI
Methodology and convergence rates for functional linear regression
TL;DR: In this paper, an alternative approach based on quadratic regularisation is suggested and shown to have advantages from some points of view, and it is shown that optimal convergence rates are achieved by the PCA technique in certain circumstances.
Journal ArticleDOI
Generalized functional linear models
TL;DR: In this paper, a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function is proposed, where a linear predictor is obtained by forming the scalar product of the predictor function with a smooth parameter function and the expected value of the response is related to this linear predictor via a link function.
Journal ArticleDOI
Smoothing splines estimators for functional linear regression
TL;DR: In this paper, a smoothing splines estimator for the functional slope parameter based on a slight modification of the usual penalty was proposed, and it was shown that these rates are optimal in the sense that they are minimax over large classes of possible slope functions and distributions of the predictive curves.
References
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Journal ArticleDOI
Sliced Inverse Regression for Dimension Reduction
TL;DR: In this article, sliced inverse regression (SIR) is proposed to reduce the dimension of the input variable without going through any parametric or nonparametric model-fitting process.
Book
Functional Data Analysis
TL;DR: This monograph presents many ideas and techniques in the functional domain of such classics as linear regression, principal components analysis, linear modelling, and canonical correlation analysis, as well as specifically functional techniques such as curve registration and principal differential analysis.
Book ChapterDOI
Functional Data Analysis
TL;DR: In this article, the authors introduce the concept of functional data analysis (FDA) to describe the smoothness of the process of generating functional data from a set of observed curves and images.