Functional linear regression analysis based on partial least squares and its application

Functional linear model with functional predictors and scalar response is a simple and popular model in the field of functional data analysis. The slope function is usually expanded on some basis functions, such as spline and functional principal component (FPC) basis, and then the model can be converted into a multivariate linear model. The FPC basis can keep most variance information of the functional data, but the correlation with response is not considered. Motivated by this, we use partial least square basis to expand the slope function. Meanwhile, considering the functional predictors are not all significant and variable selection procedure is implemented. In this process, group variable selection is introduced to identify the significant predictors. Then the proposed method is used to analyse the relationship between number of monthly emergency patients and some environmental factors in functional form, and some meaningful results are obtained.