Robust covariance estimation under L₄-L₂ norm equivalence

2018/09/27 by Shahar Mendelson, Mendelson, Shahar, Zhivotovskiy Nikita +1 · 1 citation
Engineering · Mathematics · #FOS: Mathematics #Mathematical Analysis and Transform Methods #Radar Systems and Signal Processing #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1809.10462

openalex publication_date 2018/09/27 · openalex created_date 2018/10/05 · openalex updated_date 2026/07/28

Abstract

Let X be a centered random vector taking values in ℝ^d and let Σ= 𝔼(X⊗ X) be its covariance matrix. We show that if X satisfies an L₄-L₂ norm equivalence, there is a covariance estimator Σ that exhibits the optimal performance one would expect had X been a gaussian vector. The procedure also improves the current state-of-the-art regarding high probability bounds in the subgaussian case (sharp results were only known in expectation or with constant probability). In both scenarios the new bound does not depend explicitly on the dimension d, but rather on the effective rank of the covariance matrix Σ.

Citations

• Estimation of the covariance structure of heavy-tailed distributions

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• Estimation of High-dimensional Nonlinear Vector Autoregressive Models

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