Robust stat ist ics seeks to provide methods that emulate popular stat ist ical methods, but which are not unduly af fected by out liers or other small departures f rom model assumptions. In stat ist ics, classical est imat ion methods rely heavily on assumptions which are of ten not met in pract ice. In part icular, it is of ten assumed that the data errors are normally distributed, at least a...

Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be maliciously corrupted many other ways, such as systematic measurement errors and missing covariates. We consider corruption either TV Wasserstein distance, show that robust estimation is possible whenever the true population distribution satisfies property called genera...