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Po-Ling Loh, University of Wisconsin and Madison,

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Mean estimation for entangled single-sample distributions
14 March 2019 from 3:30 PM to 4:30 PM
201 Thomas Building
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We consider the problem of estimating the common mean of univariate
data, when independent samples are drawn from non-identical symmetric,
unimodal distributions. This captures the setting where all samples
are Gaussian with different unknown variances. We propose an estimator
that adapts to the level of heterogeneity in the data, achieving
near-optimality in both the i.i.d. setting and some heterogeneous
settings, where the fraction of “low-noise" points is as small as log
n. Our estimator n is a hybrid of the modal interval, shorth, and
median estimators from classical statistics. The rates depend on the
percentile of the mixture distribution, making our estimators useful
even for distributions with infinite variance.