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Creators/Authors contains: "Strawn, Nate"

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  1. ; (, SIAM Journal on Mathematics of Data Science (SIMODS))
    This paper is devoted to the statistical properties of the geometric median, a robust measure of centrality for multivariate data, as well as its applications to the problem of mean estimation via the median of means principle. Our main theoretical results include (a) the upper bound for the distance between the mean and the median for general absolutely continuous distributions in $$\mathbb R^d$$, and examples of specific classes of distributions for which these bounds do not depend on the ambient dimension $$d$$; (b) exponential deviation inequalities for the distance between the sample and the population versions of the geometric median, which again depend only on the trace-type quantities and not on the ambient dimension. As a corollary, we deduce the improved bounds for the multivariate median of means estimator that hold for large classes of heavy-tailed distributions. 
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