  In a recent paper, Nguyen, Kuhn, and Esfahani (2018) built a distributionally
robust estimator for the precision matrix of the Gaussian distribution. The
distributional uncertainty size is a key ingredient in the construction of this
estimator. We develop a statistical theory which shows how to optimally choose
the uncertainty size to minimize the associated Stein loss. Surprisingly,
rather than the expected canonical square-root scaling rate, the optimal
uncertainty size scales linearly with the sample size.
