Generalized linear array models with applications to multidimensional smoothing

By Iain D. Currie, M. Durban, Paul H. C. Eilers. 2006

236 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b5aae55f116f31e57607ac364a243b9cc68040d0

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In Statistics and Probability

Citations in the corpus

Twenty years of P-splines (2015, methodology): “Currie et al. (2006) analysed tensor product P-splines as mixed models.”
A general framework for functional regression modelling (2017, background): “This leads to Kronecker products in the design matrix and together with the Kronecker sum penalty (3.3) results in a special case of the generalized linear array model introduced by Currie et al. (2006).”
A COMPARISON OF MIXED MODEL SPLINES FOR CURVE FITTING (2007, methodology): “These authors also extended the P-spline model to two (or more) dimensions and, in later papers, develop efficient algorithms for fitting multi-dimensional P-splines (Eilers, Currie & Durban, 2006; Currie, Durban & Eilers, 2006), although not using mixed model methods.”
Conditional transformation models (2012, methodology): “Doksum and Gasko (1990) discussed the flexibility of this class of models, and Cheng et al. (1995) introduced a generic algorithm for linear transformation model estimation, i.”
P-spline ANOVA-type interaction models for spatio-temporal smoothing (2011, methodology): “The array is flattened onto the dimension in which the constraints are applied, and reinstated in vector form (see Currie et al., 2006; Eilers et al., 2006, for software considerations).”
The functional linear array model (2015, methodology): “By defining suitable array-based linear algebra routines the number of operations required to compute effect estimates and predictions, as well as the storage requirements, are reduced dramatically (cf. Currie et al., 2006).”
Fast bivariate P‐splines: the sandwich smoother (2010, methodology): “Dierckx (1982) proposed a smoother with the same structure as (1), but our asymptotic analysis and the fast implementation for the sandwich smoother are new. For smoothing two-dimensional histograms, Eilers and Goeman (2004) studied a simplified version of the sandwich smoother with special smoother”