Suppose we are given a set of n i.i.d. samples from a Gaussian with known variance but unknown mean. We wish to estimate the mean. It is well known that the sample mean is an excellent estimator for the true mean.
However, if a small fraction of the samples are corrupted (i.e. chosen by an adversary instead of being drawn from the Gaussian), the sample mean can fail spectacularly.
In this talk, I will present an estimator which is robust to such corruptions and also show a lower bound.