Smooth design-adapted wavelets for nonparametric stochastic regression
(2001) , 26 pages
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- Abstract
- In the setting of nonparametric stochastic regression, we introduce a new way to build smooth design-adapted wavelets. Starting from the Unbalanced Haar basis, we use the lifting scheme framework to build improved biorthogonal filters. A weighted average interpolation scheme allows us to construct wavelets with a higher number of vanishing analysing moments. We include a step which stabilizes the transform by local semi- orthogonalisation. The achievement of this article is to provide a uniform solution to the usual criticisms of wavelet estimators. Indeed, our transform automatically adapts to the nature of the regression problem, that is, to the irregularity of the design, to data on the interval, and to an arbitrary sample size (which does not need to be a power of two). We propose a wavelet thresholding algorithm and show its numerical performance both on real data and simulations including white, correlated and heteroscedastic noise.
- Affiliations
Citations
Delouille, V., Simoens, J., & von Sachs, R. (2001). Smooth design-adapted wavelets for nonparametric stochastic regression (STAT Discussion Paper 0117). https://hdl.handle.net/2078.5/33548