Weyl eigenvalue asymptotics and sharp adaptation on vector bundles
This paper examines the estimation of an indirect signal embedded in white noise on vector bundles. It is found that the sharp asymptotic minimax bound is determined by the degree to which the indirect signal is embedded in the linear operator. Thus when the linear operator has polynomial decay, recovery of the signal is polynomial where the exact minimax constant and rate are determined. Adaptive sharp estimation is carried out using a blockwise shrinkage estimator. Application to the spherical deconvolution problem for the polynomially bounded case is made.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 100 (2009)
Issue (Month): 9 (October)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Healy, Dennis M. & Hendriks, Harrie & Kim, Peter T., 1998. "Spherical Deconvolution," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 1-22, October.
- Jussi Klemela, 1999. "Asymptotic Minimax Risk for the White Noise Model on the Sphere," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 465-473.
- Bissantz, Nicolai & Hohage, T. & Munk, Axel & Ruymgaart, F., 2007. "Convergence rates of general regularization methods for statistical inverse problems and applications," Technical Reports 2007,04, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
- Kim, Peter T. & Koo, Ja-Yong, 2002. "Optimal Spherical Deconvolution," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 21-42, January.
- Goldenshluger, Alexander, 2002. "Density Deconvolution in the Circular Structural Model," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 360-375, May.
- Kim, Peter T. & Koo, Ja-Yong & Park, Heon Jin, 2004. "Sharp minimaxity and spherical deconvolution for super-smooth error distributions," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 384-392, August.
- Koo, Ja-Yong & Kim, Peter T., 2008. "Sharp adaptation for spherical inverse problems with applications to medical imaging," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 165-190, February.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:100:y:2009:i:9:p:1962-1978. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.