Smoothing spline estimation of variance functions

This article considers spline smoothing of variance functions. We focus on selection of the smoothing parameters and develop three direct data-driven methods: unbiased risk (UBR), generalized approximate cross-validation (GACV), and generalized maximum likelihood (GML). In addition to guaranteed convergence, simulations show that these direct methods perform better than existing indirect UBR, generalized cross-validation (GCV), and GML methods. The direct UBR and GML methods perform better than the GACV method. An application to array-based comparative genomic hybridization data illustrates the usefulness of the proposed methods.