Sparse Precision Matrix Estimation with Calibration

We propose a semiparametric method for estimating sparse precision matrix of high dimensional elliptical distribution. The proposed method calibrates regularizations when estimating each column of the precision matrix. Thus it not only is asymptotically tuning free, but also achieves an improved finite sample performance. Theoretically, we prove that the proposed method achieves the parametric rates of convergence in both parameter estimation and model selection. We present numerical results on both simulated and real datasets to support our theory and illustrate the effectiveness of the proposed estimator.