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Multivariate spline analysis for multiplicative models: Estimation, testing and application to climate change

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  • Azaïs, Jean-Marc
  • Ribes, Aurélien

Abstract

This paper presents multiplicative, or bi-additive, models with some spline-type regularity for a rectangular array of data, for example in space and time. The one-dimensional smoothing spline model is extended to this multiplicative model including regularity in each dimension. For estimation, we prove the existence of the maximum penalized likelihood estimates (MPLEs), and introduce a numerical algorithm that converges in a weak sense to a critical point of the penalized likelihood. Explicit MPLEs are given in two important particular cases.

Suggested Citation

  • Azaïs, Jean-Marc & Ribes, Aurélien, 2016. "Multivariate spline analysis for multiplicative models: Estimation, testing and application to climate change," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 38-53.
    • Handle: RePEc:eee:jmvana:v:144:y:2016:i:c:p:38-53
    DOI: 10.1016/j.jmva.2015.09.026
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