  We apply a method recently introduced to the statistical literature to
directly estimate the precision matrix from an ensemble of samples drawn from a
corresponding Gaussian distribution. Motivated by the observation that
cosmological precision matrices are often approximately sparse, the method
allows one to exploit this sparsity of the precision matrix to more quickly
converge to an asymptotic 1/sqrt(Nsim) rate while simultaneously providing an
error model for all of the terms. Such an estimate can be used as the starting
point for further regularization efforts which can improve upon the
1/sqrt(Nsim) limit above, and incorporating such additional steps is
straightforward within this framework. We demonstrate the technique with toy
models and with an example motivated by large-scale structure two-point
analysis, showing significant improvements in the rate of convergence.For the
large-scale structure example we find errors on the precision matrix which are
factors of 5 smaller than for the sample precision matrix for thousands of
simulations or, alternatively, convergence to the same error level with more
than an order of magnitude fewer simulations.
