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Spline Smoothing over Difficult Regions

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  • Siem Jan Koopman

    ()
    (VU University Amsterdam)

  • Soon Yip Wong

    ()
    (VU University Amsterdam)

Abstract

We consider the problem of smoothing data on two-dimensional grids with holes or gaps. Such grids are often referred to as difficult regions. Since the data is not observed on these locations, the gap is not part of the domain. We cannot apply standard smoothing methods since they smooth over and across difficult regions. More unfavorable properties of standard smoothers become visible when the data is observed on an irregular grid in a non-rectangular domain. In this paper, we adopt smoothing spline methods within a state space framework to smooth data on one- or two-dimensional grids with difficult regions. We make a distinction between two types of missing observations to handle the irregularity of the grid and to ensure that no smoothing takes place over and across the difficult region. For smoothing on two-dimensional grids, we introduce a two-step spline smoothing method. The proposed solution applies to all smoothing methods that can be represented in a state space framework. We illustrate our methods for three different cases of interest.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 08-114/4.

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Date of creation: 18 Nov 2008
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Handle: RePEc:dgr:uvatin:20080114

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Web page: http://www.tinbergen.nl

Related research

Keywords: Bivariate smoothing; Geo-statistics; Missing observations; Smoothing spline model; State space methods;

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  1. A. C. Harvey & Siem Jan Koopman, 2000. "Computing Observation Weights for Signal Extraction and Filtering," Econometric Society World Congress 2000 Contributed Papers 0888, Econometric Society.
  2. 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.
  3. Gao F. & Wahba G. & Klein R. & Klein B., 2001. "Smoothing Spline ANOVA for Multivariate Bernoulli Observations With Application to Ophthalmology Data," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 127-160, March.
  4. Graham Horgan, 1999. "Using wavelets for data smoothing: A simulation study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 923-932.
  5. E. E. Kammann & M. P. Wand, 2003. "Geoadditive models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 1-18.
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