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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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    References listed on IDEAS

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    1. Ciprian Crainiceanu & David Ruppert & Gerda Claeskens & M. P. Wand, 2005. "Exact likelihood ratio tests for penalised splines," Biometrika, Biometrika Trust, vol. 92(1), pages 91-103, March.
    2. Claudia Tebaldi & Julie Arblaster, 2014. "Pattern scaling: Its strengths and limitations, and an update on the latest model simulations," Climatic Change, Springer, vol. 122(3), pages 459-471, February.
    3. Henri Caussinus & Olivier Mestre, 2004. "Detection and correction of artificial shifts in climate series," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(3), pages 405-425, August.
    4. Lu, Nelson & Zimmerman, Dale L., 2005. "The likelihood ratio test for a separable covariance matrix," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 449-457, July.
    5. Jean‐Baptiste Denis & John C. Gower, 1996. "Asymptotic Confidence Regions for Biadditive Models: Interpreting Genotype‐Environment Interactions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(4), pages 479-493, December.
    6. Ohlson, Martin & Rauf Ahmad, M. & von Rosen, Dietrich, 2013. "The multilinear normal distribution: Introduction and some basic properties," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 37-47.
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