Fast and compact smoothing on large multidimensional grids

Authors:
Paul H. C. Eilers;Iain D. Currie;Maria Durbán
Affiliations:
Department of Medical Statistics, Leiden University Medical Centre, P.O. Box 9604, 2300 RC Leiden, The Netherlands;Heriot-Watt University, Edinburgh, Scotland;Universidad Carlos III de Madrid, Madrid, Spain
Venue:
Computational Statistics & Data Analysis
Year:
2006

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Abstract

A framework of penalized generalized linear models and tensor products of B-splines with roughness penalties allows effective smoothing of data in multidimensional arrays. A straightforward application of the penalized Fisher scoring algorithm quickly runs into storage and computational difficulties. A novel algorithm takes advantage of the special structure of both the data as an array and the model matrix as a tensor product; the algorithm is fast, uses only a moderate amount of memory and works for any number of dimensions. Examples are given of how the method is used to smooth life tables and image data.