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Po Ling Loh
Mean estimation for entangled single-sample distributions
Add to Calendar 2019-08-14T19:30:00 2019-08-14T20:30:00 UTC Mean estimation for entangled single-sample distributions Thomas Bldg
Start DateWed, Aug 14, 2019
3:30 PM
End DateWed, Aug 14, 2019
4:30 PM
Presented By
Po-Ling Loh, University of Wisconsin and Madison

We consider the problem of estimating the common mean of univariatedata, when independent samples are drawn from non-identical symmetric,unimodal distributions. This captures the setting where all samplesare Gaussian with different unknown variances. We propose an estimatorthat adapts to the level of heterogeneity in the data, achievingnear-optimality in both the i.i.d. setting and some heterogeneoussettings, where the fraction of "low-noise" points is as small as logn. Our estimator n is a hybrid of the modal interval, shorth, andmedian estimators from classical statistics. The rates depend on thepercentile of the mixture distribution, making our estimators usefuleven for distributions with infinite variance.