Abstract
This chapter treats in more detail the adaptivity property of nonlinear (thresholded) wavelet estimates. We first introduce different modifications and generalizations of soft and hard thresholding. Then we develop the notion of adaptive estimators and present the results about adaptivity of wavelet thresholding for density estimation problems. Finally, we consider the data-driven methods of selecting the wavelet basis, the threshold value and the initial resolution level, based on Stein’s principle. We finish by a discussion of oracle inequalities and miscellaneous related topics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Härdle, W., Kerkyacharian, G., Picard, D., Tsybakov, A. (1998). Wavelet thresholding and adaptation. In: Wavelets, Approximation, and Statistical Applications. Lecture Notes in Statistics, vol 129. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2222-4_11
Download citation
DOI: https://doi.org/10.1007/978-1-4612-2222-4_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98453-7
Online ISBN: 978-1-4612-2222-4
eBook Packages: Springer Book Archive