Smooth design-adapted wavelets for nonparametric stochastic regression

• 成果类型: Article
• 署名作者: Delouille, V; Simoens, J; von Sachs, R
• 署名单位: Rice University; Universite Catholique Louvain; Universite Catholique Louvain
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214504000000971
• 发表日期: 2004
• 页码: 643-658
• 关键词: Shrinkage

摘要

We treat nonparametric stochastic regression using smooth design-adapted wavelets built by means of the lifting scheme. The proposed method automatically adapts to the nature of the regression problem, that is, to the irregularity of the design, to data on the interval, and to arbitrary sample sizes (which do not need to be a power of 2). As such, this method provides a uniform solution to the usual criticisms of first-generation wavelet estimators. More precisely, starting from the unbalanced Haar basis orthogonal with respect to the empirical design measure, we use weighted average interpolation to construct biorthogonal wavelets with a higher number of vanishing analyzing moments. We include a lifting step that improves the conditioning through constrained local semiorthogonalization. We propose a wavelet thresholding algorithm and show its numerical performance both on real data and in simulations including white, correlated, and heteroscedastic noise.