THE EVIL OF SUPEREFFICIENCY

We discuss the intriguing notion of statistical superefficiency in a s traightforward manner with a minimum of formality. We point out that f or any given parameter estimator there exist other estimators which ha ve a strictly lower asymptotic variance and hence are statistically mo re efficient than the former. In particular, if the former estimator w as statistically efficient (in the sense that its asymptotic variance was equal to the Cramer-Rao bound) then the latter estimators could be called ''superefficient''. Among others, the phenomenon of supereffic iency implies that asymptotically there exists no uniformly minimum-va riance parameter estimator.