Functional Principal Component Regression Model Based on FIrst-order Boosting and Model Averaging

Abstract

Functional regression model has always been an important research direction in the field of functional data analysis, in which functional principal component analysis as a common method of functional regression modeling, the determination of the number of truncations of the eigenfunctions has always been a problem to be solved. Based on this, this paper proposes a functional principal component regression model based on the idea of model averaging, which uses Bayesian model averaging instead of model selection, determines the number of truncations adaptively and balances the prediction error with the training error. In addition, the original function curves do not effectively capture the information of their functional characteristics. In this paper, the first-order derivative function is used as the supplementary information of the original function curve to jointly characterize the predictor variables. In the efficiency test, this paper averages the Bayesian model as the benchmark model and conducts real data analysis on several benchmark datasets. The results show that the proposed method has higher predictive accuracy and robustness than commonly used models.