Functional Bayesian Model Average Regression Based on Derivative Information

Abstract

Functional data regression models based on basis function expansion have been widely used in economic, financial, and environmental fields. However, determining the appropriate type and quantity of basis functions, such as KL expansion and B-spline, has remained a challenge to overcome. Additionally, when two curves are similar, constructing an effective regression model can prove to be difficult. On top of that, this paper suggests a functional Bayesian model average regression model, which is based on the KL expansion of the derivative function. On the one hand, the method uses the first and second-order derivative function information as predictors to capture the curve's fluctuation trend more comprehensively. On the other hand, the method applies model averaging to dynamically determine the appropriate number of basis functions to use, which can effectively alleviate the overfitting and underfitting problems of the model. The experiments and corresponding data analysis demonstrate that the proposed method has higher prediction accuracy and robustness than the comparative methods.