Hybrid local polynomial wavelet shrinkage: wavelet regression with automatic boundary adjustment

Abstract

An usual assumption underlying the use of wavelet shrinkage is that the regression function is assumed to be either periodic or symmetric. However, such an assumption is not always realistic. This paper proposes an effective method for correcting the boundary bias introduced by the inappropriateness of such periodic or symmetric assumption. The idea is to combine wavelet shrinkage with local polynomial regression, where the latter regression technique is known to possess excellent boundary properties. Simulation results from both the univariate and bivariate settings provide strong evidence that the proposed method is extremely effective in terms of correcting boundary bias.