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Generalized linear array models with applications to multidimensional smoothing

Author

Listed:
  • I. D. Currie
  • M. Durban
  • P. H. C. Eilers

Abstract

Data with an array structure are common in statistics, and the design or regression matrix for analysis of such data can often be written as a Kronecker product. Factorial designs, contingency tables and smoothing of data on multidimensional grids are three such general classes of data and models. In such a setting, we develop an arithmetic of arrays which allows us to define the expectation of the data array as a sequence of nested matrix operations on a coefficient array. We show how this arithmetic leads to low storage, high speed computation in the scoring algorithm of the generalized linear model. We refer to a generalized linear array model and apply the methodology to the smoothing of multidimensional arrays. We illustrate our procedure with the analysis of three data sets: mortality data indexed by age at death and year of death, spatially varying microarray background data and disease incidence data indexed by age at death, year of death and month of death. Copyright 2006 Royal Statistical Society.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jorssb:v:68:y:2006:i:2:p:259-280
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    References listed on IDEAS

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    1. Lancelot F. James & Antonio Lijoi & Igor Prünster, 2009. "Posterior Analysis for Normalized Random Measures with Independent Increments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 76-97.
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    4. Aldous, David J., 1981. "Representations for partially exchangeable arrays of random variables," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 581-598, December.
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    8. A. Athreya & C. E. Priebe & M. Tang & V. Lyzinski & D. J. Marchette & D. L. Sussman, 2016. "A Limit Theorem for Scaled Eigenvectors of Random Dot Product Graphs," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(1), pages 1-18, February.
    9. Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2007. "Controlling the reinforcement in Bayesian non-parametric mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 715-740.
    10. Isobel Claire Gormley & Thomas Brendan Murphy, 2006. "Analysis of Irish third-level college applications data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(2), pages 361-379.
    11. Leisen, Fabrizio & Lijoi, Antonio, 2011. "Vectors of two-parameter Poisson-Dirichlet processes," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 482-495, March.
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