Estimation on semi-functional linear errors-in-variables models

Abstract

Semi-functional linear regression models are important in practice. In this paper, their estimation is discussed when function-valued and real-valued random variables are all measured with additive error. By means of functional principal component analysis and kernel smoothing techniques, the estimators of the slope function and the non parametric component are obtained. To account for errors in variables, deconvolution is involved in the construction of a new class of kernel estimators. The convergence rates of the estimators of the unknown slope function and non parametric component are established under suitable norm and conditions. Simulation studies are conducted to illustrate the finite sample performance of our method.

Keywords:

• Functional data
• Semi-functional linear models
• Errors-in-variables
• Functional principal component analysis

Additional information

Funding

The research was supported in part by National Natural Science Foundation of China (11571112), the National Social Science Foundation Key Program (17ZDA091) and the 111 Project of China (B14019).