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Fast algorithm for smoothing parameter selection in multidimensional generalized P-splines

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  • María Xosé Rodríguez-Álvarez
  • Dae-Jin Lee
  • Thomas Kneib
  • María Durbán
  • Paul Eilers
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    Abstract

    A new computational algorithm for estimating the smoothing parameters of a multidimensional penalized spline generalized model with anisotropic penalty is presented. This new proposal is based on the mixed model representation of a multidimensional P-spline, in which the smoothing parameter for each covariate is expressed in terms of variance components. On the basis of penalized quasi-likelihood methods (PQL), closed-form expressions for the estimates of the variance components are obtained. This formulation leads to an efficient implementation that can considerably reduce the computational load. The proposed algorithm can be seen as a generalization of the algorithm by Schall (1991) - for variance components estimation - to deal with non-standard structures of the covariance matrix of the random effects. The practical performance of the proposed computational algorithm is evaluated by means of simulations, and comparisons with alternative methods are made on the basis of the mean square error criterion and the computing time. Finally, we illustrate our proposal with the analysis of two real datasets: a two dimensional example of historical records of monthly precipitation data in USA and a three dimensional one of mortality data from respiratory disease according to the age at death, the year of death and the month of death

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    Bibliographic Info

    Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws133026.

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    Date of creation: Sep 2013
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    Handle: RePEc:cte:wsrepe:ws133026

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    Keywords: Smoothing; P-splines; Tensor product; Anisotropic penalty; Mixed Models;

    References

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    1. Simon N. Wood, 2011. "Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 3-36, January.
    2. I. D. Currie & M. Durban & P. H. C. Eilers, 2006. "Generalized linear array models with applications to multidimensional smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 259-280.
    3. Eilers, Paul H.C. & Currie, Iain D. & Durban, Maria, 2006. "Fast and compact smoothing on large multidimensional grids," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 61-76, January.
    4. Simon N. Wood, 2003. "Thin plate regression splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 95-114.
    5. X. Lin & D. Zhang, 1999. "Inference in generalized additive mixed modelsby using smoothing splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 381-400.
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