Interpolation methods for nonlinear wavelet regression with irregularly spaced design

• 成果类型: Article
• 署名作者: Hall, P; Turlach, BA
• 署名单位: Australian National University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 1912-1925
• 关键词: DENSITY-ESTIMATION; shrinkage; threshold; kernel

摘要

We introduce interpolation methods that enable nonlinear wavelet estimators to be employed with stochastic design, or nondyadic regular design, in problems of nonparametric regression. This approach allows relatively rapid computation, involving dyadic approximations to wavelet-after-interpolation techniques. New types of interpolation are described, enabling first-order variance reduction at the expense of second-order increases in bias. The effect of interpolation on threshold choice is addressed, and appropriate thresholds are suggested for error distributions with as few as four finite moments.