Optimal convergence rates and asymptotic efficiency of point estimators under truncated distribution families

For regular and irregular truncated distribution families, the optimal convergence rates of consistent point estimators have been found and the corresponding asymptotic efficiencies established. Also, it has been justified that commonly used estimators are all efficient. The efficiencies here are compared to the efficiencies of asymptotically median unbiased estimators, providing a lot of counter estimator examples such that those estimators are efficient in the former sense, but not in the latter.