The Mean Estimation of the Combined Quantities by the Asymptotic Minimax Optimization

Abstract

The mean value estimation for the output quantity of combined random variables is one of the major issues in measurement. In this paper, a new quantile-based maximum likelihood estimation (QMLE) method for mean value estimation is proposed. It fuses the concept of both empirical and symmetric quantile to incorporate the order statistics into the QMLE. Unlike Sample mean derived basing only on the maximum likelihood criterion, the QMLE also considers MMSE defined using the quasi symmetric quantiles (QSQ), i.e., the first- and last-order samples. Simulation results confirm that the proposed QMLE mean estimator outperforms the conventional Sample mean estimator. This work also gives a looking-up table for the refinement corresponding to the QSQ adjustments.