Automatic polynomial wavelet regression

In Oh, Naveau and Lee (2001) a simple method is proposed for reducing the bias at the boundaries for wavelet thresholding regression. The idea is to model the regression function as a sum of wavelet basis functions and a low-order polynomial. The latter is expected to account for the boundary problem. Practical implementation of this method requires the choice of the order of the low-order polynomial, as well as the wavelet thresholding value. This paper proposes two automatic methods for making such choices. Finite sample performances of these two methods are evaluated via numerical experiments.