Minimum Variance and Minimum Kulback-Leibler Mean Estimation with a Known Quantile

This work compares two mean estimators, MV and MKL, which incorporate information about a known quantile. MV minimizes variance and MKL minimizes Kulback-Leibler divergence. Both estimators are asymptotically equivalent and normally distributed but differ at finite sample sizes. Monte-Carlo simulation studies show that MV has higher mean squared error than MKL in the majority of simulated scenarios. Authors recommend using MKL when a quantile of an underlying distribution is known.