Functional quasi-likelihood regression models with smooth random effects

Jeng-Min Chiou, Hans-Georg Müller, Jane-Ling Wang

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2003 · Volume 65 · Issue 2

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).

Keywords

Estimating equations, Functional data analysis, Functional regression, Principal components, Semiparametric quasi-likelihood regression, Single-index model, Smoothing

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