Date of this Version
Journal of the American Statistical Association
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.
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.
Adaptive confidence band, average coverage, coverage probability, excess mass, lower bounds, noncovered points, nonparametric regression, wavelets, white noise model
Cai, T., Low, M. G., & Ma, Z. (2014). Adaptive Confidence Bands for Nonparametric Regression Functions. Journal of the American Statistical Association, 109 (507), 1054-1070. http://dx.doi.org/10.1080/01621459.2013.879260
Date Posted: 27 November 2017