Before revision:  It provides a sparse/weakly sparse and consistent estimate of the precision matrix , using the Lasso method. We analyze three issues. One of the key results in our paper is that mean-variance efficiency for the portfolios in large dimensions is established. Then tied to that result , we also show that the maximum out-of-sample Sharpe ratio can be consistently estimated in this large portfolio of assets.
After revision:  It provides a sparse/weakly sparse and consistent estimate of the precision matrix of errors as a new method. Next, we show that the residual-based nodewise regression provides a consistent estimate for the precision matrix of errors. In another new development , we also show that the maximum out-of-sample Sharpe ratio can be consistently estimated in this large portfolio of assets.