Smoothing spline estimation of variance functions

Anna Liu, Tiejun Tong, Yuedong Wang*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

17 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)312-329
Number of pages18
JournalJournal of Computational and Graphical Statistics
Issue number2
Publication statusPublished - Jun 2007

User-Defined Keywords

  • Array-based comparative genomic hybridization
  • Generalized approximate cross-validation
  • Generalized maximum likelihood
  • Heteroscedasticity
  • Smoothing parameter
  • Unbiased risk


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