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Multiscale Poisson data smoothing

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  • Maarten Jansen

Abstract

Summary. The paper introduces a framework for non‐linear multiscale decompositions of Poisson data that have piecewise smooth intensity curves. The key concept is conditioning on the sum of the observations that are involved in the computation of a given multiscale coefficient. Within this framework, most classical wavelet thresholding schemes for data with additive homoscedastic noise can be used. Any family of wavelet transforms (orthogonal, biorthogonal or second generation) can be incorporated in this framework. Our second contribution is to propose a Bayesian shrinkage approach with an original prior for coefficients of this decomposition. As such, the method combines the advantages of the Haar–Fisz transform with wavelet smoothing and (Bayesian) multiscale likelihood models, with additional benefits, such as extendability towards arbitrary wavelet families. Simulations show an important reduction in average squared error of the output, compared with the present techniques of Anscombe or Fisz variance stabilization or multiscale likelihood modelling.

Suggested Citation

  • Maarten Jansen, 2006. "Multiscale Poisson data smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 27-48, February.
  • Handle: RePEc:bla:jorssb:v:68:y:2006:i:1:p:27-48
    DOI: 10.1111/j.1467-9868.2005.00531.x
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    Cited by:

    1. Fryzlewicz, Piotr, 2008. "Data-driven wavelet-Fisz methodology for nonparametric function estimation," LSE Research Online Documents on Economics 25165, London School of Economics and Political Science, LSE Library.
    2. Fryzlewicz, Piotr & Delouille, V´eronique & Nason, Guy P., 2007. "GOES-8 X-ray sensor variance stabilization using the multiscale data-driven Haar-Fisz transform," LSE Research Online Documents on Economics 25221, London School of Economics and Political Science, LSE Library.
    3. Maarten Jansen & Guy P. Nason & B. W. Silverman, 2009. "Multiscale methods for data on graphs and irregular multidimensional situations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 97-125, January.

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