Robust estimation for boundary correction in wavelet regression

Abstract

For boundary problems present in wavelet regression, two common methods are usually considered: polynomial wavelet regression (PWR) and hybrid local polynomial wavelet regression (LPWR). Normality assumption played a key role for making such choices for the order of the low-order polynomial, the wavelet thresholding value and other calculations involved in LPWR. However, in practice, the normality assumption may not be valid. In this paper, for PWR, we propose three automatic robust methods based on: MM-estimator, bootstrap and robust threshold procedure. For LPWR, the use of a robust local polynomial (RLP) estimator with a robust threshold procedure has been investigated. The proposed methods do not require any knowledge of noise distribution, are easy to implement and achieve high performances when only a small amount of data is in hand. A simulation study is conducted to assess the numerical performance of the proposed methods.

Keywords:

• boundary region
• MM-estimator
• bootstrap
• robust threshold
• simulation

Mathematics Subject Classification :

• 37M05
• 62G35
• 62G08
• 65T60

Acknowledgements

This research is supported by Universiti Sains Malaysia.