  Let $X$ be a random variable with unknown mean and finite variance. We
present a new estimator of the mean of $X$ that is robust with respect to the
possible presence of outliers in the sample, provides tight sub-Gaussian
deviation guarantees without any additional assumptions on the shape or tails
of the distribution, and moreover is asymptotically efficient. This is the
first estimator that provably combines all these qualities in one package. Our
construction is inspired by robustness properties possessed by the
self-normalized sums. Theoretical findings are supplemented by numerical
simulations highlighting strong performance of the proposed estimator in
comparison with previously known techniques.
