Fast smoothing parameter separation in multidimensional generalized P-splines: the SAP algorithm

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• 作者：María Xosé Rodríguez-álvarez ; Dae-Jin Lee ; Thomas Kneib…
• 关键词：Smoothing ; P ; splines ; Tensor product ; Anisotropic penalty ; Mixed models
• 刊名：Statistics and Computing
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：25
• 期：5
• 页码：941-957
• 全文大小：1,649 KB
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• 作者单位：María Xosé Rodríguez-álvarez (1)
  Dae-Jin Lee (2) (3)
  Thomas Kneib (4)
  María Durbán (5)
  Paul Eilers (6)
  
  1. Department of Statistics and Operations Research, University of Vigo, Campus Lagoas-Marcosende s/n, 36310?, Vigo, Spain
  2. CSIRO Computational Informatics, Clayton, VIC, Australia
  3. BCAM - Basque Center for Applied Mathematics, Bilbao, Spain
  4. Chair of Statistics, Georg-August-Universit?t G?ttingen, G?ttingen, Germany
  5. Department of Statistics, Universidad Carlos III de Madrid, Leganés, Spain
  6. Erasmus Medical Center, Rotterdam, The Netherlands
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics Computing and Software
  Statistics
  Numeric Computing
  Mathematics
  Artificial Intelligence and Robotics
  
• 出版者：Springer Netherlands
• ISSN：1573-1375

文摘

A new computational algorithm for estimating the smoothing parameters of a multidimensional penalized spline generalized linear 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, closed-form expressions for the estimates of the variance components are obtained. This formulation leads to an efficient implementation that considerably reduces the computational burden. 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 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.