Covariate-Adjusted Precision Matrix Estimation Under Lower Polynomial Moment Assumption

Multiple regression analysis has a wide range of applications. The analysis of error structures in regression model Y=ΓX+Z has also attracted much attention. This paper focuses on large-scale precision matrix of the error vector that only has lower polynomial moments. We mainly study upper bounds of the proposed estimator under different norms in term of the probability estimation. It is shown that our estimator achieves the same optimal convergence order as under Gaussian assumption on the data. Simulation experiments further validate that our method has advantages.