Covariance Estimation under Missing Observations and L_4-L_2 Moment Equivalence

05/22/2023

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by   Pedro Abdalla, et al.

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We consider the problem of estimating the covariance matrix of a random vector by observing i.i.d samples and each entry of the sampled vector is missed with probability p. Under the standard L_4-L_2 moment equivalence assumption, we construct the first estimator that simultaneously achieves optimality with respect to the parameter p and it recovers the optimal convergence rate for the classical covariance estimation problem when p=1