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Confidence sets for nonparametric wavelet regression
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DOI：10.1214/009053605000000011.png)
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Abstract
En 中文
We construct nonparametric confidence sets for regression functions using wavelets that are uniform over Besov balls. We consider both thresholding and modulation estimators for the wavelet coefficients. The confidence set is obtained by showing that a pivot process, constructed from the loss function, converges uniformly to a mean zero Gaussian process. Inverting this pivot yields a confidence set for the wavelet coefficients, and from this we obtain confidence sets on functionals of the regression curve.
Keywords:
confidence sets
Stein's unbiased risk estimator
nonparametric regression
thresholding
wavelets
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