Abstract: For functional regression model，a more general semi-parameteric model are proposed，this model can overcome the disdvantage of parametric model and nonparametric model，and obtain more robust estimate. We study the parameter estimation problem in functional part of the linear additive models and the asymptotic properties of estimators，it promotes the relevant results in the existing literature simultaneously.

Key words: functional data, B -spline, L_1/2 regularization, convergence speed