An alternative bandwidth selection method for estimating functional coefficient models

Abstract

Functional coefficient regression models are very useful for many statistics and economics applications and there exists a large body of literature on kernel estimation of the coefficient functions. Fan and Zhang (1999) point out that the traditional estimation method is not optimal if the coefficient functions possess different degrees of smoothness. They propose a two-step method to attenuate the drawback. To apply the two-step method, one needs to identify which coefficient function is the smoothest one and undersmooth all other functions in the first stage. In this paper we propose an alternative approach which assigns each smooth function a different bandwidth and we choose the bandwidths simultaneously. Simulation results show that our proposed method compare well with existing methods.