Estimating the Risk of Stabilized Hard Thresholding for Inverse Statistical Problems in Models with Long-Range Dependences

This work considers a means of stabilized hard thresholding for inverting linear homogeneous operators using wavelet decomposition. The unbiased mean squared risk estimate for this procedure is analyzed using a data model with additive Gaussian noise. Assuming there is a long-range dependence among noise coefficients, conditions are given that ensure strong consistency and asymptotic normality of the unbiased risk estimator.