Automatic bandwidth choice and confidence intervals in nonparametric regression

• 成果类型: Article
• 署名作者: Neumann, MH
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1995
• 页码: 1937-1959
• 关键词: resampling methods; DENSITY-ESTIMATION; bootstrap; jackknife

摘要

In the present paper we combine the issues of bandwidth choice and construction of confidence intervals in nonparametric regression. Main emphasis is put on fully data-driven methods. We modify the root n-consistent bandwidth selector of Hardle, Hall and Marron such that it is appropriate for heteroscedastic data, and we show how one can optimally choose the bandwidth g of the pilot estimator <(m)over cap(g)>. Then we consider classical confidence intervals based on kernel estimators with data-driven bandwidths and compare their coverage accuracy. We propose a method to put undersmoothing with a data-driven bandwidth into practice and show that this procedure outperforms explicit bias correction.