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Functional quasi‐likelihood regression models with smooth random effects
Author(s) -
Chiou JengMin,
Müller HansGeorg,
Wang JaneLing
Publication year - 2003
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00393
Subject(s) - mathematics , covariate , nonparametric regression , variance function , statistics , semiparametric regression , regression analysis , random function , regression , parametric statistics , functional principal component analysis , functional data analysis , random variable
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).