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Robust estimators, like the median of a point set, are important for dataanalysis in the presence of outliers. We study robust estimators forlocationally uncertain points with discrete distributions. That is, each pointin a data set has a discrete probability distribution describing its location.The probabilistic nature of uncertain data makes it challenging to compute suchestimators, since the true value of the estimator is now described by adistribution rather than a single point. We show how to construct and estimatethe distribution of the median of a point set. Building the approximate supportof the distribution takes near-linear time, and assigning probability to thatsupport takes quadratic time. We also develop a general approximation techniquefor distributions of robust estimators with respect to ranges with bounded VCdimension. This includes the geometric median for high dimensions and theSiegel estimator for linear regression.

Approximating the Distribution of the Median and other Robust Estimators on Uncertain Data