An alternative bandwidth selection method for estimating functional coefficient models

• We propose a new bandwidth selection method for estimating varying coefficient models.
• Our method allows for different amount of smoothing for different coefficient function.
• Our method does not require one to know which coefficient function is the smoothest one.
• Simulation results show that our method compare well with existing methods.

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.