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Multiscale methods for data on graphs and irregular multidimensional situations
Author(s) -
Jansen Maarten,
Nason Guy P.,
Silverman B. W.
Publication year - 2009
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2008.00672.x
Subject(s) - shrinkage , wavelet , computer science , parametric statistics , dimension (graph theory) , spatial analysis , shrinkage estimator , wavelet transform , representation (politics) , algorithm , function (biology) , data mining , pattern recognition (psychology) , artificial intelligence , mathematics , machine learning , statistics , mean squared error , minimum variance unbiased estimator , politics , evolutionary biology , law , bias of an estimator , pure mathematics , political science , biology
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.