  We present simple differentially private estimators for the mean and
covariance of multivariate sub-Gaussian data that are accurate at small sample
sizes. We demonstrate the effectiveness of our algorithms both theoretically
and empirically using synthetic and real-world datasets -- showing that their
asymptotic error rates match the state-of-the-art theoretical bounds, and that
they concretely outperform all previous methods. Specifically, previous
estimators either have weak empirical accuracy at small sample sizes, perform
poorly for multivariate data, or require the user to provide strong a priori
estimates for the parameters.
