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Confidence Sets for Nonparametric Wavelet Regression

Christopher R. Genovese and Larry Wasserman

Abstract:

We construct nonparametric confidence sets for regression functions using wavelets. 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 functional of the regression curve.



Keywords: Confidence sets, Stein's unbiased risk estimator, nonparametric regression, thresholding, wavelets



Heidi Sestrich 2002-09-05
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