Tiger: A tuning-insensitive approach for optimally estimating gaussian graphical models

We propose a new procedure for estimating high dimensional Gaussian graphical models. Our approach is asymptotically tuning-free and non-asymptotically tuning-insensitive: it requires very few efforts to choose the tuning parameter in finite sample settings. Computationally, our procedure is significantly faster than existing methods due to its tuning-insensitive property. Theoretically, the obtained estimator is simulta-neously minimax optimal for precision matrix estimation under different norms. Em-pirically, we illustrate the advantages of our method using thorough simulated and real examples. The R package bigmatrix implementing the proposed methods is available on the Comprehensive R Archive Network