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3620 South Vermont Avenue, Los Angeles, CA 90089
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Meeting ID: 946 3846 8773
University of Wisconsin, Madison
Abstract: Mean and location estimation are two of the most fundamental problems in statistics. How do we most accurately estimate the mean of a distribution, given i.i.d. samples? What if we additionally know the shape of the distribution, and we only need to estimate its translation/location?
Both problems have well-established asymptotic theories: use the sample mean for mean estimation and maximum likelihood for location estimation. Yet, asymptotic guarantees can sometimes be misleading in practice: it may take arbitrarily many samples to converge to the (law of large numbers) limit, depending on how bad the underlying distribution is, especially if we want high confidence in our estimate.
In this talk, I will discuss recent progress on developing finite sample and high probability theories for these problems that yield optimal constants. Results include new mean estimators in 1-dimensional and very-high dimensional regimes with error tight up to a 1+o(1) factor, as well as new characterizations of location estimation and improvements over the MLE. I will end by describing some directions for future work in this area.
This talk is based on joint works with Paul Valiant, Shivam Gupta and Eric Price.
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