The Frobenius loss |$|| \Delta {\boldsymbol \Psi }||_{\rm F}$| for our toy model as a function of sample size d for the sample precision matrix (blue circles), our estimate of the precision matrix with and without the intermediate smoothing step (green diamonds and orange squares, respectively). The latter two cases assume a banding of k = 3. The dashed lines show a d^−1/2 trend which is more quickly attained by the estimates presented in this work than by the sample precision matrix. Recall that this is a 100 × 100 matrix – one cannot estimate the sample precision matrix with d < 100. This restriction is not present for the estimator presented here; all that is required is that d > k.