Generalized linear array models with applications to multidimensional smoothing
AbstractData 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society Series B.
Volume (Year): 68 (2006)
Issue (Month): 2 ()
Contact details of provider:
Postal: 12 Errol Street, London EC1Y 8LX, United Kingdom
Web page: http://wileyonlinelibrary.com/journal/rssb
More information through EDIRC
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- 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.
- repec:wyi:journl:002174 is not listed on IDEAS
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Nolde, Natalia & Parker, Gary, 2014. "Stochastic analysis of life insurance surplus," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 1-13.
- 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.
- Aris Perperoglou, 2011. "Fitting survival data with penalized Poisson regression," Statistical Methods and Applications, Springer, vol. 20(4), pages 451-462, November.
- 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.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.