In the sublinear sparsity limit the ML estimator achieves vanishing squared error below a noise threshold that coincides with the converse bound for constant-amplitude signals, proving asymptotic optimality of separable Bayesian estimators.
T he horse- shoe estimator: Posterior concentration around nearly bla ck vectors,
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Direct and Converse Theorems in Estimating Signals with Sublinear Sparsity
In the sublinear sparsity limit the ML estimator achieves vanishing squared error below a noise threshold that coincides with the converse bound for constant-amplitude signals, proving asymptotic optimality of separable Bayesian estimators.