Weyl eigenvalue asymptotics and sharp adaptation on vector bundles

Peter T. Kim, Ja-Yong Koo and Zhi-Ming Luo

Journal of Multivariate Analysis, 2009, vol. 100, issue 9, 1962-1978

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.

Keywords: Eigenstructure; Laplacian; Pinsker-Weyl; bound; Riemannian; geometry; Sobolev; ellipsoid; Spectral; geometry; Weyl; constant (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (3)

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