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Semi-supervised wavelet shrinkage

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  • Lee, Kichun
  • Vidakovic, Brani

Abstract

To estimate a possibly multivariate regression function g under the general regression setup, y=g+ϵ, one can use wavelet thresholding as an alternative to conventional nonparametric regression methods. Wavelet thresholding is a simple operation in the wavelet domain that selects a subset of coefficients corresponding to an estimator of g when back-transformed. We propose an enhancement to wavelet thresholding by selecting a subset in a semi-supervised fashion in which the neighboring structure and classification function appropriate for wavelet domains are utilized. Wavelet coefficients are classified into two types: labeled, which have either strong or weak magnitudes, and unlabeled, which have in-between magnitudes. Both are connected to neighboring coefficients and belong to a low-dimensional manifold within the set of all wavelet coefficients. The decision to include a coefficient in the model depends not only on its magnitude but also on the labeled and the unlabeled coefficients from its neighborhood. We discuss the theoretical properties of the method and demonstrate its performance in simulated examples.

Suggested Citation

  • Lee, Kichun & Vidakovic, Brani, 2012. "Semi-supervised wavelet shrinkage," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1681-1691.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1681-1691
    DOI: 10.1016/j.csda.2011.10.010
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    References listed on IDEAS

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    1. Antoniadis, Anestis & Bigot, Jeremie & Sapatinas, Theofanis, 2001. "Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 6(i06).
    2. Iain M. Johnstone & Bernard W. Silverman, 1997. "Wavelet Threshold Estimators for Data with Correlated Noise," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 319-351.
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