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Generalized linear array models with applications to multidimensional smoothing

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

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    Bibliographic Info

    Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society Series B.

    Volume (Year): 68 (2006)
    Issue (Month): 2 ()
    Pages: 259-280

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    Handle: RePEc:bla:jorssb:v:68:y:2006:i:2:p:259-280

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    Cited by:
    1. Hofer, Vera & Krempl, Georg, 2013. "Drift mining in data: A framework for addressing drift in classification," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 377-391.
    2. Sabine Schnabel & Paul Eilers, 2013. "Simultaneous estimation of quantile curves using quantile sheets," AStA Advances in Statistical Analysis, Springer, vol. 97(1), pages 77-87, January.
    3. Welham, S.J. & Thompson, R., 2009. "A note on bimodality in the log-likelihood function for penalized spline mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 920-931, February.
    4. Lee, Dae-Jin & Durbán, María, 2009. "Smooth-CAR mixed models for spatial count data," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2968-2979, June.
    5. Dae-Jin Lee & Maria Durban, 2008. "Smooth-car mixed models for spatial count data," Statistics and Econometrics Working Papers ws085820, Universidad Carlos III, Departamento de Estadística y Econometría.
    6. Tomas, Julien & Planchet, Frédéric, 2013. "Multidimensional smoothing by adaptive local kernel-weighted log-likelihood: Application to long-term care insurance," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 573-589.
    7. Dae-Jin Lee & María Durbán, 2012. "Seasonal modulation mixed models for time series forecasting," Statistics and Econometrics Working Papers ws122519, Universidad Carlos III, Departamento de Estadística y Econometría.
    8. Dae-Jin Lee & Maria Durban, 2009. "P-spline anova-type interaction models for spatio-temporal smoothing," Statistics and Econometrics Working Papers ws093312, Universidad Carlos III, Departamento de Estadística y Econometría.
    9. Heim, S. & Fahrmeir, L. & Eilers, P.H.C. & Marx, B.D., 2007. "3D space-varying coefficient models with application to diffusion tensor imaging," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6212-6228, August.
    10. Aris Perperoglou, 2011. "Fitting survival data with penalized Poisson regression," Statistical Methods and Applications, Springer, vol. 20(4), pages 451-462, November.
    11. repec:wyi:journl:002174 is not listed on IDEAS
    12. Nolde, Natalia & Parker, Gary, 2014. "Stochastic analysis of life insurance surplus," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 1-13.
    13. María Xosé Rodríguez-Álvarez & Dae-Jin Lee & Thomas Kneib & María Durbán & Paul Eilers, 2013. "Fast algorithm for smoothing parameter selection in multidimensional generalized P-splines," Statistics and Econometrics Working Papers ws133026, Universidad Carlos III, Departamento de Estadística y Econometría.
    14. Thomas Kneib & Bernhard Baumgartner & Winfried Steiner, 2007. "Semiparametric multinomial logit models for analysing consumer choice behaviour," AStA Advances in Statistical Analysis, Springer, vol. 91(3), pages 225-244, October.

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