%AZhu, Banghua%AJiao, Jiantao%ASteinhardt, Jacob%D2020%I %K %MOSTI ID: 10175220 %PMedium: X %TWhen Does the Tukey Median Work? %XWe analyze the performance of the Tukey median estimator under total variation (TV) distance corruptions. Previous results show that under Huber's additive corruption model, the breakdown point is 1/3 for high-dimensional halfspace-symmetric distributions. We show that under TV corruptions, the breakdown point reduces to 1/4 for the same set of distributions. We also show that a certain projection algorithm can attain the optimal breakdown point of 1/2. Both the Tukey median estimator and the projection algorithm achieve sample complexity linear in dimension. Country unknown/Code not availableOSTI-MSA