Efficient estimation in varying coefficient regression models

Abstract

Varying coefficient models have been studied for many years, and local kernel estimation is an important method to estimate the coefficient functions. Since same bandwidth parameter is used for each coefficient function, local kernel estimation is not effective when the degree of smoothness is different for each coefficient function. In this paper, a new global estimation method based on kernel function and backfitting is proposed. In this method, different bandwidth parameters can be used for each coefficient function to improve the estimation accuracy, and asymptotic properties of the estimators are proved. To reduce the computational complexity, an adaptive global estimation method, which is based on an estimation of the bandwidth ratio and has only one bandwidth parameter to be selected, is proposed. Simulation results show that the proposed methods work well, and two real data examples further demonstrate the potential of the proposed methods.

KEYWORDS:

• Varying coefficient model
• local kernel estimation
• global estimation
• asymptotic properties

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Social Science Foundation of China (No. 21BTJ044), the Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX22$\mathrm{\_}$1615) and the National Natural Science Foundation of China (No. 11971240).