Adaptive Confidence Bands for Nonparametric Regression Functions
Tony Cai, Mark Low, and Zongming Ma
-
Abstract:
A new formulation for the construction of adaptive confidence bands in nonparametric function estimation problems is proposed. Confidence bands are constructed which have size that adapts to the smoothness of the function while guaranteeing that 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 is small. It is shown that the bands adapt over a maximum range of Lipschitz classes. The procedure can be easily modified and used for other nonparametric function estimation models.
- Paper:
pdf file.
- Other related papers:
Cai, T. and Low, M. (2004).
An adaptation theory for nonparametric confidence intervals.
The Annals of Statistics 32, 1805-1840.Cai, T. & Low, M. (2006).
Adaptive confidence balls.
The Annals of Statistics 34, 202-228.Cai, T., Low, M. and Xia, Y. (2013).
Adaptive confidence intervals for regression functions under shape constraints.
The Annals of Statistics 42, 722-750.