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Functional quasi-likelihood regression models with smooth random effects. (English) Zbl 1065.62065
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).

MSC:
62G08 Nonparametric regression and quantile regression
62P10 Applications of statistics to biology and medical sciences; meta analysis
65C60 Computational problems in statistics (MSC2010)
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