 Adaptive Confidence Bands for Nonparametric Regression FunctionsT. Tony Cai, Mark Low and Zongming Ma Journal of the American Statistical Association, 2014, vol. 109, issue 507, 1054-1070 Abstract: This article proposes a new formulation for the construction of adaptive confidence bands (CBs) in nonparametric function estimation problems. CBs, which have size that adapts to the smoothness of the function while guaranteeing that both the relative excess mass of the function lying outside the band and the measure of the set of points where the function lies outside the band are small. It is shown that the bands adapt over a maximum range of Lipschitz classes. The adaptive CB can be easily implemented in standard statistical software with wavelet support. We investigate the numerical performance of the procedure using both simulated and real datasets. The numerical results agree well with the theoretical analysis. The procedure can be easily modified and used for other nonparametric function estimation models. Supplementary materials for this article are available online. Date: 2014 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlasa:v:109:y:2014:i:507:p:1054-1070 Ordering information: This journal article can be ordered from DOI: 10.1080/01621459.2013.879260 Access Statistics for this article Journal of the American Statistical Association is currently edited by Xuming He, Jun Liu, Joseph Ibrahim and Alyson Wilson More articles in Journal of the American Statistical Association from Taylor & Francis Journals |
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