Generalized resilience and robust statistics
广义韧性与稳健统计
Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be maliciously corrupted in many other ways, such as systematic measurement errors and missing covariates. We consider corruption in either TV or Wasserstein distance, and show that robust estimation is possible whenever the true population distribution satisfies a property called generalized resilience, which holds under moment or hypercontractive…