Statistics Papers

Document Type

Journal Article

Date of this Version

2014

Publication Source

Journal of the American Statistical Association

Volume

109

Issue

507

Start Page

1054

Last Page

1070

DOI

10.1080/01621459.2013.879260

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 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 confidence band can be easily implemented in standard statistical software with wavelet support. Numerical performance of the procedure is investigated 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.

Copyright/Permission Statement

This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 14 Jan 2014, available online: http://wwww.tandfonline.com/10.1080/01621459.2013.879260.

Keywords

Adaptive confidence band, average coverage, coverage probability, excess mass, lower bounds, noncovered points, nonparametric regression, wavelets, white noise model

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Date Posted: 27 November 2017