An adaptive estimator of location based on the t-family

For estimating the location of a continuous symmetric distribution, we consider the maximum likelihood estimate of location in a location-scale-tailweight family based on the t-distributions. The idea is to obtain an asymptotically efficient estimator of location within a parametric family large enough to contain members close to the normal tailweight, as well as members with heavy tails. This is the “partially adaptive” idea of Bickel (1982). Ve present Monte Carlo results comparing this estimator to several competitors, particularly with one due to Hogg which motivated our idea.