Asymptotic Risk and Bayes Risk of Thresholding and Superefficient Estimates and Optimal Thresholding

The classic superefficient estimate of Hodges for a one dimensional normal mean and the modern hard thresholding estimates introduced in the works of David Donoho and Iain Johnstone exhibit some well known risk phenomena. They provide quantifiable improvement over the MLE near zero, but also suffer from risk inflation suitably away from zero. Classic work of Le Cam and Hájek has precisely pinned down certain deep and fundamental aspects of these risk phenomena.