Sharp minimaxity and spherical deconvolution for super-smooth error distributions

Authors:
Peter T. Kim;Ja-Yong Koo;Heon Jin Park
Affiliations:
Department of Mathematics and Statistics, University of Guelph, Guelph, Ont., Canada NIG 2WI;Inha University, Incheon, South Korea;Inha University, Incheon, South Korea
Venue:
Journal of Multivariate Analysis
Year:
2004

Citing 5
Cited 2

Asymptotic methods in statistical theory

Asymptotic methods in statistical theory
Spherical deconvolution

Journal of Multivariate Analysis
MiniMax Methods for Image Reconstruction

MiniMax Methods for Image Reconstruction
Optimal spherical deconvolution

Journal of Multivariate Analysis
Density deconvolution in the circular structural model

Journal of Multivariate Analysis

Weyl eigenvalue asymptotics and sharp adaptation on vector bundles

Journal of Multivariate Analysis
The dictionary approach for spherical deconvolution

Journal of Multivariate Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

The spherical deconvolution problem was first proposed by Rooij and Ruymgaart (in: G. Roussas (Ed.), Nonparametric Functional Estimation and Related Topics, Kluwer Academic Publishers, Dordrecht, 1991, pp. 679-690) and subsequently solved in Healy et al. (J. Multivariate Anal. 67 (1998) 1). Kim and Koo (J. Multivauriate Anal. 80 (2002) 21) established minimaxity in the L2-rate of convergence. In this paper, we improve upon the latter and establish sharp minimaxity under a super-smooth condition on the error distribution.