Sparse precision matrix estimation under lower polynomial moment assumption

Abstract

Precision matrix (inverse covariance matrix) estimation is a rising challenge in contemporary applications while dealing with high‐dimensional data. This paper focuses on large‐scale precision matrix of the random vector that only has lower polynomial moments. We mainly investigate upper bounds of the proposed estimator under the spectral norm in terms of the probability and mean estimation respectively. It is shown that the data‐driven estimator is fully adaptive and achieves the same optimal convergence order as under Gaussian assumption on the data. Simulation studies further support our theoretical claims.