The Estimation Of Semi-Functional Linear Model

With the continuous development of science and technology, the collected data in real life are mostly functional data. It reflects wider application prospects to study functional data. At present, the studies of functional data has caused the attention of academic cir-cles at home and abroad. This paper aims at resolving the estimation of Semi-Functional Linear Model in mixed functional data with the aid of Functional Principal Component Analysis (FPCA) and Smoothing Spline. First, FPCA is employed to simplify func-tional linear part in this model. Then the proposed B-spline method is to approximate Non-parametric part of Semi-Functional Linear Model. To estimate the coefficients of functional part and Non-parameteric part, the Least-Squares technique is leveraged. Fur-thermore, under several regular conditions, we present convergence rate for the above two part and the consistency of variance estimation. Finally, we use statistical simulations to evaluate the performance of the estimation.