A note on P-spline additive models with correlated errors
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.
scientific article; zbMATH DE number 2118513
scientific article