Multiscale methods for data on graphs and irregular multidimensional situations

M Jansen, GP Nason, BW Silverman

Research output: Contribution to journalArticle (Academic Journal)peer-review

65 Citations (Scopus)


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.
Translated title of the contributionMuLtiscale methods for data on graphs and irregular multidimensional situations
Original languageEnglish
Pages (from-to)97 - 125
Number of pages30
JournalJournal of the Royal Statistical Society: Series B
Issue number1
Early online date16 Sept 2008
Publication statusPublished - Jan 2009

Bibliographical note

Publisher: Wiley


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