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

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  • Hee-Seok Oh
  • Douglas W. Nychka
  • Thomas C. M. Lee

Abstract

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. Copyright 2007, Oxford University Press.

Suggested Citation

  • Hee-Seok Oh & Douglas W. Nychka & Thomas C. M. Lee, 2007. "The Role of Pseudo Data for Robust Smoothing with Application to Wavelet Regression," Biometrika, Biometrika Trust, vol. 94(4), pages 893-904.
    • Handle: RePEc:oup:biomet:v:94:y:2007:i:4:p:893-904
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    File URL: http://hdl.handle.net/10.1093/biomet/asm064
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    Cited by:

    1. Alsaidi M. Altaher & Mohd Tahir Ismail, 2012. "Robust Wavelet Estimation to Eliminate Simultaneously the Effects of Boundary Problems, Outliers, and Correlated Noise," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-18, November.
    2. Zlatana Nenova & Jennifer Shang, 2022. "Chronic Disease Progression Prediction: Leveraging Case‐Based Reasoning and Big Data Analytics," Production and Operations Management, Production and Operations Management Society, vol. 31(1), pages 259-280, January.
    3. Graciela Boente & Alejandra Martínez & Matías Salibián-Barrera, 2017. "Robust estimators for additive models using backfitting," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 744-767, October.
    4. Lee, Jong Soo & Cox, Dennis D., 2010. "Robust smoothing: Smoothing parameter selection and applications to fluorescence spectroscopy," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3131-3143, December.
    5. Yaeji Lim & Hee-Seok Oh, 2015. "Simultaneous confidence interval for quantile regression," Computational Statistics, Springer, vol. 30(2), pages 345-358, June.
    6. McGinnity, K. & Varbanov, R. & Chicken, E., 2017. "Cross-validated wavelet block thresholding for non-Gaussian errors," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 127-137.
    7. Monica Pratesi & M. Ranalli & Nicola Salvati, 2009. "Nonparametric -quantile regression using penalised splines," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(3), pages 287-304.

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