Sieve M-estimator for a semi-functional linear model

We propose sieve M-estimator for a semi-functional linear model in which the scalar response is explained by a linear operator of functional predictor and smooth functions of some real-valued random variables. Spline estimators of the functional coefficient and the smooth functions are considered, and by selecting appropriate knot numbers the optimal convergence rate and the asymptotic normality can be obtained under some mild conditions. Some simulation results and a real data example are presented to illustrate the performance of our estimation method.