Confidence sets for nonparametric wavelet regression

By Christopher R. Genovese, Larry A. Wasserman. 2005

51 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Media Technology

View Paper: https://www.semanticscholar.org/paper/e86e7a0f7075a16a4fbd1d33d0f5d34ed87e05c6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Ian W. McKeague
2. Moulinath Banerjee
3. Tommaso Cai
4. Mark G. Low
5. Larry A. Wasserman
6. Christopher R. Genovese

In Computer Vision and Pattern Recognition

1. Ian W. McKeague
2. Moulinath Banerjee
3. Tommaso Cai
4. Mark G. Low
5. Larry A. Wasserman
6. Christopher R. Genovese
7. Adam D. Bull

In Media Technology

1. Ian W. McKeague
2. Moulinath Banerjee
3. Tommaso Cai
4. Mark G. Low
5. Larry A. Wasserman
6. Christopher R. Genovese

Citations in the corpus

• Confidence sets for split points in decision trees (2007, methodology): “Such an approach was originally suggested by Stein [19] for a multivariate normal mean and has recently been used by Genovese and Wasserman [8] for nonparametric wavelet regression.”
• Adaptive Confidence Balls (2006, background): “See, for example, [8], where such an approach is taken.”
• Adaptive confidence bands (2007, background): “Moreover, a minimal amount of smoothness is required to ensure that σ̂ consistently estimates σ; see Genovese and Wasserman (2005).”
• An adaptation theory for nonparametric confidence intervals (2004, background): “On the other hand Li (1989), Beran and Dümbgen (1998) and Genovese and Wasserman (2002) have constructed confidence balls which guarantee coverage probability.”
• CONFIDENCE BANDS IN DENSITY ESTIMATION (2010, unknown): “We refer to Li (1989), Beran and Dümbgen (1998), Hoffman and Lepski (2002), Juditsky and Lambert-Lacroix (2003), Baraud (2004), Genovese and Wasserman (2005), Cai and Low (2006) and Robins and van der Vaart (2006).”