Polynomial wavelet regression with boundary correction

Abstract

Wavelet regression has been proven to be highly effective at reconstructing most kinds of regression curves. However, this estimator suffers from boundary problems caused by the application of the wavelet transformation to a finite signal, giving large bias estimation at the edges. To overcome these problems, different approaches have been proposed, in which wavelet shrinkage was used as a combination with a low order polynomial model. In this paper, polynomial wavelet regression is considered. A simulation study is conduct to evaluate the achievement of polynomial wavelet regression using a variety of test functions, threshold selection methods and noise structures. We use five different kinds of errors: Normal, Normal mixture, long tail and errors from first order autoregressive and moving average models. Five thresholding selection methods are used: Universal, Sure, two fold cross validation, Ebayes and level dependent cross validation.