A semi-parametric bootstrap-based best linear unbiased estimator of location under symmetry

In this note we provide a novel semi-parametric best linear unbiased estimator (BLUE) of location and its corresponding variance estimator under the assumption the random variate is generated from a symmetric location-scale family of distributions. The approach follows in a two-stage fashion and is based on the exact bootstrap estimate of the covariance matrix of the order statistic. We generalize our approach to add a robustness component in order to derive a trimmed BLUE of location under a semi-parametric symmetry assumption.