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Weyl eigenvalue asymptotics and sharp adaptation on vector bundles
- Authors
- Kim, Peter T.; Koo, Ja-Yong; Luo, Zhi-Ming
- Issue Date
- 10월-2009
- Publisher
- ELSEVIER INC
- Keywords
- Eigenstructure; Laplacian; Pinsker-Weyl bound; Riemannian geometry; Sobolev ellipsoid; Spectral geometry; Weyl constant
- Citation
- JOURNAL OF MULTIVARIATE ANALYSIS, v.100, no.9, pp.1962 - 1978
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF MULTIVARIATE ANALYSIS
- Volume
- 100
- Number
- 9
- Start Page
- 1962
- End Page
- 1978
- ISSN
- 0047-259X
- Abstract
- 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. (C) 2009 Elsevier Inc. All rights reserved.
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