Robust Covariance Matrix Estimation via Matrix Depth

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Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates (2018, methodology): “This proof is essentially the same as the lower bound in the robust mean estimation literature (Chen et al., 2015, Lai et al., 2016).”
Robust estimation via robust gradient estimation (2018, methodology): “A complementary line of recent research [9, 10] has focused on providing minimax upper and lower bounds on the performance of estimators under ε-contamination model, without the constraint of computational tractability.”
Robust regression via mutivariate regression depth (2017, methodology): “The convergence rate of Ω̂ jj is given by [7].”
Computationally Efficient Robust Sparse Estimation in High Dimensions (2017, methodology): “Future directions of research include developing faster alternatives to the ellipsoid algorithm, to further relax the assumptions in various settings, and finally to close the gap in sample complexity to statistically optimal, albeit computationally intractable procedures (Chen et al., 2015, 2016).”
Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (2016, methodology): “For example, besides those mentioned by Professors Paul and Wang, Chen et al. (2013) considered estimation of sparse covariance and precision matrices in a high-dimensional stationary process setting with autocovariance of any lag k ≥ 1 treated as nuisance parameters.”