Model selection using wavelet decomposition and applications

• 成果类型: Article
• 署名作者: Antoniadis, A; Gijbels, I; Gregoire, G
• 署名单位: Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Universite Catholique Louvain
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/84.4.751
• 发表日期: 1997
• 页码: 751763
• 关键词: GOODNESS-OF-FIT; Nonparametric Regression; linear-model; prediction; variables; INFORMATION; criteria; Cusum; ORDER

摘要

In this paper we discuss how to use wavelet decompositions to select a regression model. The methodology relies on a minimum description length criterion which is used to determine the number of nonzero coefficients in the vector of wavelet coefficients. Consistency properties of the selection rule are established and simulation studies reveal information on the distribution of the minimum description length selector. We then apply the selection rule to specific problems, including testing for pure white noise. The power of this test is investigated via simulation studies and the selection criterion is also applied to testing for no effect in nonparametric regression.