The minimax rate for estimating μ^T Σ^{-1} μ under sparsity of Σ^{-1} μ is (s log p)/n + 1/√n, attained by a debiased ℓ1-regularized plug-in estimator.
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Optimal estimation of functionals of high-dimensional mean and covariance matrix
The minimax rate for estimating μ^T Σ^{-1} μ under sparsity of Σ^{-1} μ is (s log p)/n + 1/√n, attained by a debiased ℓ1-regularized plug-in estimator.