The DOI matches its Crossref record; 65 of the 65 references it cites were found in a registry or an index.
Regularization of Wavelet Approximations
Abstract
In this paper, we introduce nonlinear regularized wavelet estimators for estimating nonparametric regression functions when sampling points are not uniformly spaced. The approach can apply readily to many other statistical contexts. Various new penalty functions are proposed. The hard-thresholding and soft-thresholding estimators of Donoho and Johnstone are specific members of nonlinear regularized wavelet estimators. They correspond to the lower and upper envelopes of a class of the penalized least squares estimators. Necessary conditions for penalty functions are given for regularized estimators to possess thresholding properties. Oracle inequalities and universal thresholding parameters are obtained for a large class of penalty functions. The sampling properties of nonlinear regularized wavelet estimators are established and are shown to be adaptively minimax. To efficiently solve penalized least squares problems, nonlinear regularized Sobolev interpolators (NRSI) are proposed as initial estimators, which are shown to have good sampling properties. The NRSI is further ameliorated by regularized one-step estimators, which are the one-step estimators of the penalized least squares problems using the NRSI as initial estimators. The graduated nonconvexity algorithm is also introduced to handle penalized least squares problems. The newly introduced approaches are illustrated by a few numerical examples.
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Cites
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Sure Independence Screening for Ultrahigh Dimensional Feature Space
Fan, J., & Lv, J. (2008) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2008.00674.x · Cited by 2,711
Self-citationChallenges of Big Data analysis
Fan, J., Han, F., & Liu, H. (2014) · National Science Review · doi:10.1093/nsr/nwt032 · Cited by 1,482
Shrinkage Fields for Effective Image Restoration
Schmidt, U., & Roth, S. (2014) · 2014 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2014.349 · Cited by 543
Variable selection in nonparametric additive models
Huang, J., Horowitz, J. L., & Wei, F. (2010) · The Annals of Statistics · doi:10.1214/09-aos781 · Cited by 537
Fan, J., & Li, R. (2004) · Journal of the American Statistical Association · doi:10.1198/016214504000001060 · Cited by 437
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Metadata
- Authors
- Antoniadis, A., & Fan, J.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2001-09
- Volume
- 96
- Issue
- 455
- Pages
- 939-967
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W1972163814
- Cited by
- 498
- References
- 65
- FWCI
- 10.65
- Type
- journal article
- Language
- en
- Open access
- closed
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