Adaptive confidence interval for pointwise curve estimation

• 成果类型: Article
• 署名作者: Picard, D; Tribouley, K
• 署名单位: Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2000
• 页码: 298-335
• 关键词: density; bounds

摘要

We present a procedure associated with nonlinear wavelet methods that provides adaptive confidence intervals around f(x(0)), in either a white noise model or a regression setting. A suitable modification in the truncation rule for wavelets allows construction of confidence intervals that achieve optimal coverage accuracy up to a logarithmic factor. The procedure does not require knowledge of the regularity of the unknown function f; it is also efficient for functions with a low degree of regularity.