A note on P-spline additive models with correlated errors
type: Item
instance of: scholarly article
title: A note on P-spline additive models with correlated errors
zbMATH Open document ID: 1050.62042
author: Iain D. Currie
author: María Durbán
published in: Computational Statistics
publication date: 2004-11-24T00:00:00Z
review text: The model under consideration is an additive model where the response variable \(y\) is represented as a sum of \(k\) smooth terms which act on the explanatory variables \(x_1,\dots,x_k\): \[ y=\alpha+ f_1(x_1)+\dots+f_k(x_k)+\varepsilon, \qquad E(f_i(x_i))=0, \] in the presence of correlated Gaussian errors. The authors use the penalized spline (P-spline) approach of \textit{P. H. C. Eilers} and \textit{B. D. Marx} [Stat. Sci. 11, No. 2, 89--121 (1996; Zbl 0955.62562)] to estimate \(f_i(.)\), \(i=1,\dots,k\), and give simple expressions for the estimated curves \(f_i\). These expressions give the possibility to calculate confidence intervals for each fitted function. At the same time, the mixed model representation of P-splines gives an efficient method for both the estimation of the smoothing and correlation parameters and enables one to use likelihood ratio tests for model selection. The obtained results are applied to the analysis of some electricity consumption data.
Mathematics Subject Classification ID: 62G08
Mathematics Subject Classification ID: 62-08
Mathematics Subject Classification ID: 62J12
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 2118513
zbMATH Keywords: additive model
zbMATH Keywords: penalized spline
zbMATH Keywords: back-fitting
zbMATH Keywords: serial correlation
zbMATH Keywords: mixed model
zbMATH Keywords: autoregression model
zbMATH Keywords: model selection
zbMATH Keywords: estimation
describes a project that uses: S-PLUS
describes a project that uses: MEMSS
MaRDI profile type: Publication
full work available at URL: s001800300143
OpenAlex ID: W10028449
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DOI: 10.1007/S001800300143
description: scientific article; zbMATH DE number 2118513