Functional quasi‐likelihood regression models with smooth random effects

Jeng‐Min Chiou, Hans‐Georg Müller and Jane‐Ling Wang

Journal of the Royal Statistical Society Series B, 2003, vol. 65, issue 2, 405-423

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).

Date: 2003
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