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Multiscale methods for data on graphs and irregular multidimensional situations

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  • Maarten Jansen
  • Guy P. Nason
  • B. W. Silverman

Abstract

Summary. For regularly spaced one‐dimensional data, wavelet shrinkage has proven to be a compelling method for non‐parametric function estimation. We create three new multiscale methods that provide wavelet‐like transforms both for data arising on graphs and for irregularly spaced spatial data in more than one dimension. The concept of scale still exists within these transforms, but as a continuous quantity rather than dyadic levels. Further, we adapt recent empirical Bayesian shrinkage techniques to enable us to perform multiscale shrinkage for function estimation both on graphs and for irregular spatial data. We demonstrate that our methods perform very well when compared with several other methods for spatial regression for both real and simulated data. Although we concentrate on multiscale shrinkage (regression) we present our new ‘wavelet transforms’ as generic tools intended to be the basis of methods that might benefit from a multiscale representation of data either on graphs or for irregular spatial data.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:71:y:2009:i:1:p:97-125
    DOI: 10.1111/j.1467-9868.2008.00672.x
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    References listed on IDEAS

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    2. 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.
    3. Timmermans, Catherine & Fryzlewicz, Piotr, 2012. "Shah: Shape-Adaptive Haar Wavelet Transform For Images With Application To Classification," LIDAM Discussion Papers ISBA 2012015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    6. Timmermans, Catherine & von Sachs, Rainer, 2013. "BAGIDIS: Statistically investigating curves with sharp local patterns using a new functional measure of dissimilarity," LIDAM Discussion Papers ISBA 2013031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Guy P. Nason & James L. Wei, 2022. "Quantifying the economic response to COVID‐19 mitigations and death rates via forecasting purchasing managers' indices using generalised network autoregressive models with exogenous variables," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1778-1792, October.

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