An optimal L-statistics quantile estimator for a set of location-scale populations

This paper presents an L-statistics quantile estimator for estimating the pth quantile of a population which belongs to a set of location-scale distributions. The design of the weight vector of the estimator is formulated as a constrained optimization problem. The objective of the optimization problem is to minimize the mean square error. The optimization problem is subject to a unitary constraint on the weight vector of the L-statistics quantile estimation. We solve the optimization problem and obtain an optimal solution, which is the weight vector of the proposed estimator.