Abstract: We consider a novel partially linear additive functional regression model in which both a functional predictor and some scalar predictors appear. The functional part has a semiparametric continuously additive form, while the scalar predictors appear in the linear part. The functional part has the optimal convergence rate, and the asymptotic normality of the nonfunctional part is also shown. Simulations and an empirical analysis of a Covid-19 data set demonstrate the performance of the proposed estimator.

Key words and phrases: Convergence rate, functional data, penalization, RKHS.