Weighted Estimation of the Location Parameter of a Symmetric Stable Distribution : Theory and Methods

We propose a class of weighted estimators of the location parameter of a symmetric stable distribution, where the weights decrease exponentially as a function of the scaled absolute deviation of observations from the sample median. The proposed weighted mean outperforms both the unweighted sample mean and the median for stable symmetric distributions with stability index 1 < 2, and outperforms the optimal trimmed mean for the Cauchy distribution.