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Weyl eigenvalue asymptotics and sharp adaptation on vector bundles

Authors
Kim, Peter T.Koo, Ja-YongLuo, 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
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/119164
DOI
10.1016/j.jmva.2009.03.012
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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