  We study the revenue maximization problem with an imprecisely estimated
distribution of a single buyer or several independent and identically
distributed buyers given that this estimation is not far away from the true
distribution. We use the earth mover's distance to capture the estimation error
between those two distributions in terms of both values and their
probabilities, i.e., the error in value space given a quantile, and the error
in quantile space given a value. We give explicit characterization of the
optimal mechanisms for the single buyer setting. For the multi-buyer case, we
provide an algorithm that finds an approximately optimal mechanism (FPTAS)
among the family of second price auctions with a fixed reserve.
