Robust and efficient mean estimation: an approach based on the properties of self-normalized sums

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