VISUAL ERROR CRITERIA FOR QUALITATIVE SMOOTHING

• 成果类型: Article
• 署名作者: MARRON, JS; TSYBAKOV, AB
• 署名单位: Sorbonne Universite; Universite Catholique Louvain; Universite Catholique Louvain; Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2291060
• 发表日期: 1995
• 页码: 499-507
• 关键词: DENSITY-ESTIMATION

摘要

An important gap, between the classical mathematical theory and the practice and implementation of nonparametric curve estimation, is due to the fact that the usual norms on function spaces measure something different from what the eye can see visually in a graphical presentation. Mathematical error criteria that more closely follow ''visual impression'' are developed and analyzed from both graphical and mathematical viewpoints. Examples from wavelet regression and kernel density estimation are considered.