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Spline smoothing over difficult regions

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  • Tim Ramsay

Abstract

Summary. It is occasionally necessary to smooth data over domains in ℝ2 with complex irregular boundaries or interior holes. Traditional methods of smoothing which rely on the Euclidean metric or which measure smoothness over the entire real plane may then be inappropriate. This paper introduces a bivariate spline smoothing function defined as the minimizer of a penalized sum‐of‐squares functional. The roughness penalty is based on a partial differential operator and is integrated only over the problem domain by using finite element analysis. The method is motivated by and applied to two sample smoothing problems and is compared with the thin plate spline.

Suggested Citation

  • Tim Ramsay, 2002. "Spline smoothing over difficult regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 307-319, May.
    • Handle: RePEc:bla:jorssb:v:64:y:2002:i:2:p:307-319
    DOI: 10.1111/1467-9868.00339
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    References listed on IDEAS

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    1. Graham Horgan, 1999. "Using wavelets for data smoothing: A simulation study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 923-932.
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