Covariance estimation with direction dependence accuracy

2024/02/13 by Pedro Pugliesi Abdalla, Shahar Mendelson, Abdalla, Pedro +1
Computer Science · #Direction-of-Arrival Estimation Techniques #Blind Source Separation Techniques #Speech and Audio Processing

paper · pdf · doi:10.48550/arxiv.2402.08288

Abstract

We construct an estimator \widehatΣ for covariance matrices of unknown, centred random vectors X, with the given data consisting of N independent measurements X₁,...,X_N of X and the wanted confidence level. We show under minimal assumptions on X, the estimator performs with the optimal accuracy with respect to the operator norm. In addition, the estimator is also optimal with respect to direction dependence accuracy: ⟨ \widehatΣu,u⟩ is an optimal estimator for σ²(u)=𝔼⟨ X,u⟩² when σ²(u) is ``large".

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