Functional polynomial multiple-index model

Abstract

Functional polynomial multiple-index model which includes the functional linear model, functional quadratic model and functional single index model as the special cases is considered. In this paper we propose an iterative technique to estimate the link function and polynomial coefficients nonparametrically. Simulations show that the proposed methods have good prediction performances. The proposed model is also illustrated with tecator data.

Keywords:

• Functional polynomial regression model
• Functional principal components
• Multiple index model

AMS(2000) subject classifications:

• 62J99
• 62E20

Additional information

Funding

Tao Zhang’s research was partially supported by National Natural Science Foundation of China (Grant No. 11861014,11561006), and Natural Science Foundation of Guangxi (2018JJA110013).