Adaptive nonparametric regression on spin fiber bundles
The construction of adaptive nonparametric procedures by means of wavelet thresholding techniques is now a classical topic in modern mathematical statistics. In this paper, we extend this framework to the analysis of nonparametric regression on sections of spin fiber bundles defined on the sphere. This can be viewed as a regression problem where the function to be estimated takes as its values algebraic curves (for instance, ellipses) rather than scalars, as usual. The problem is motivated by many important astrophysical applications, concerning, for instance, the analysis of the weak gravitational lensing effect, i.e. the distortion effect of gravity on the images of distant galaxies. We propose a thresholding procedure based upon the (mixed) spin needlets construction recently advocated by Geller and Marinucci (2008, 2010) and Geller et al. (2008, 2009), and we investigate their rates of convergence and their adaptive properties over spin Besov balls.
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): 104 (2012)
Issue (Month): 1 (February)
|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.:
- Baldi, Paolo & Marinucci, Domenico, 2007. "Some characterizations of the spherical harmonics coefficients for isotropic random fields," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 490-496, March.
- Kim, Peter T. & Koo, Ja-Yong & Luo, Zhi-Ming, 2009. "Weyl eigenvalue asymptotics and sharp adaptation on vector bundles," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1962-1978, October.
- Kim, Peter T. & Koo, Ja-Yong, 2002. "Optimal Spherical Deconvolution," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 21-42, January.
- Gérard Kerkyacharian & Dominique Picard & Lucien Birgé & Peter Hall & Oleg Lepski & Enno Mammen & Alexandre Tsybakov & G. Kerkyacharian & D. Picard, 2000. "Thresholding algorithms, maxisets and well-concentrated bases," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 283-344, December.
- 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:104:y:2012:i:1:p:16-38. 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.