Statistical inverse estimation in Hilbert scales
SIAM Journal on Applied Mathematics
Journal of Multivariate Analysis
Optimal spherical deconvolution
Journal of Multivariate Analysis
Density deconvolution in the circular structural model
Journal of Multivariate Analysis
Semi-Supervised Learning on Riemannian Manifolds
Machine Learning
Sharp minimaxity and spherical deconvolution for super-smooth error distributions
Journal of Multivariate Analysis
Sharp adaptation for spherical inverse problems with applications to medical imaging
Journal of Multivariate Analysis
SIAM Journal on Numerical Analysis
Adaptive nonparametric regression on spin fiber bundles
Journal of Multivariate Analysis
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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.