Locally adaptive regression splines

• 成果类型: Article
• 署名作者: Mammen, E; van de Geer, S
• 署名单位: Ruprecht Karls University Heidelberg; Leiden University; Leiden University - Excl LUMC
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 387-413
• 关键词: Nonparametric regression; wavelet shrinkage; MULTIVARIATE

摘要

Least squares penalized regression estimates with total variation penalties are considered. It is shown that these estimators are least squares splines with locally data adaptive placed knot points. The definition of these variable knot splines as minimizers of global functionals can be used to study their asymptotic properties. In particular, these results imply that the estimates adapt well to spatially inhomogeneous smoothness. We show rates of convergence in bounded variation function classes and discuss pointwise limiting distributions. An iterative algorithm based on stepwise addition and deletion of knot points is proposed and its consistency proved.