Functional data regression model based on basis function expansion and Group Lasso

In the analysis of functional data, functional data regression is a crucial statistical model. The preceding step is to smooth the discrete function, usually using the basis function expansion method. However, due to the diversity of basic functions, it is a difficult problem to choose the basis function suitable for specific data. In view of this, an adaptive basis function expansion function regression model based on Group LASSO is proposed in this paper, which is suitable for the scenario where the predictor is a random function and the response variable is a continuous scalar. The proposed method uses a variety of basis function expansion methods, significantly expands the function space, and can smooth complex random functions better than a single basis function expansion method. On the other hand, to avoid the overfitting problem caused by the over-complexity of the prediction function, this paper adopts the Group LASSO method to automatically select the best type of basis function to alleviate the overfitting problem. The effectiveness of the proposed method is verified by an empirical study on the NIR reflectance spectral datasets of meat and corn samples. The results show that the proposed method has smaller mean square error and absolute error and is robust compared with the functional regression model with single basis function expansion.