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Biometrika Advance Access originally published online on November 19, 2007
Biometrika 2007 94(4):893-904; doi:10.1093/biomet/asm064
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© 2007 Biometrika Trust

Articles

The Role of Pseudo Data for Robust Smoothing with Application to Wavelet Regression

Hee-Seok Oh

Department of Statistics, Seoul National University, Seoul 151-747, Korea heeseok{at}stats.snu.ac.kr

Douglas W. Nychka

Geophysical Statistics Project, National Center for Atmospheric Research, Boulder, Colorado 80307, U.S.A. nychka{at}ucar.edu

Thomas C. M. Lee

Department of Statistics, The Chinese University of Hong Kong, Shatin, Hong Kong, China tlee{at}sta.cuhk.edu.hk

Received for publication 1 November 2005. Revision received 1 March 2007.

We propose a robust curve and surface estimator based on M-type estimators and penalty-based smoothing. This approach also includes an application to wavelet regression. The concept of pseudo data, a transformation of the robust additive model to the one with bounded errors, is used to derive some theoretical properties and also motivate a computational algorithm. The resulting algorithm, termed the es-algorithm, is computationally fast and provides a simple way of choosing the amount of smoothing. Moreover, it is easily described, straightforwardly implemented and can be extended to other wavelet regression settings such as irregularly spaced data and image denoising. Results from a simulation study and real data examples demonstrate the promising empirical properties of the proposed approach.

Key Words: ES-algorithm • M-estimation • Penalized least-squares • Pseudo data • Robust smoothing • Wavelets



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