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Activity Number: 669 - Recent Advances in Nonparametric Statistics
Type: Contributed
Date/Time: Thursday, August 3, 2017 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract #323289
Title: A New Nonparametric Estimator of a Location Shift
Author(s): Su Chen*
Companies: University of Memphis
Keywords: mean ; kernel ; location ; nonparametric ; heavy-tailed distributions

Mean (or expected value) is a measurement of central tendency. However, it does not exist for some heavy-tailed distributions such as the Cauchy. The undefined or infinite mean of these heavy-tailed distributions explains the unreasonably large variance and bias in the sample mean, which, in turn, make all related statistical inference methods unreliable. We define kth-order mean (different from kth moment), which is 'always' finite and proportional to the natural location parameter of the underlying distribution for an appropriate choice of k. Then we propose a new nonparametric location shift estimator namely 'Kernel Weighted Average" (KWA). It is shown that the KWA estimator has a smaller empirical MSE than other existing location shift estimators such as the mean, the median and the Hodges-Lehmann (HL) estimator for heavy-tailed distributions, such as the Cauchy distribution.

Authors who are presenting talks have a * after their name.

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