Sharp minimaxity and spherical deconvolution for super-smooth error distributions

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. Multivariate 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.