Abstract: The scalar-on-function regression is quite useful for modelling mixed-data in the context of scalar and functional variables. Under this class of regression, the paper aims at proposing a compelling alternative to model selection methods to address model selection uncertainty. The considered models characterize a scalar response using parametric effect of the scalar predictors and nonparametric effect of a functional predictor, and a model averaging estimation is developed based on Mallows-type criterion to assign weights for averaging. Further, the asymptotic optimality of the resulting estimator, in terms of achieving the smallest possible squared error loss, is established. Besides, simulation studies demonstrate its superiority to or comparability with some information criterion score-based model selection and averaging estimators. The proposed procedure is also applied to a mid-infrared spectra dataset for illustration.

Key words and phrases: Functional data, mallows-type criterion, model average.