Multiscale methods for data on graphs and irregular multidimensional situations

• 成果类型: Article
• 署名作者: Jansen, Maarten; Nason, Guy P.; Silverman, B. W.
• 署名单位: University of Bristol; KU Leuven; University of Oxford
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2008.00672.x
• 发表日期: 2009
• 页码: 97-125
• 关键词: wavelet transforms; lifting-scheme; regularization; regression; shrinkage; threshold; algorithm; selection

摘要

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.