51 Remarks about Super-Efficiency The problem here is not due to irregularities of the density function,but due to the partialness of our estimator to uo =0. This example shows that no regularity conditions on the density can prevent an estimator from violating (3).This possibility can only be avoided by placing restrictions on the sequence of estimators. LeCam (1953)showed that for any sequence of estimators satisfying (2),the set of points in violating (3)has Lebesgue measure zero. ●Superefficiency shows that“parametric”models can be useful and justified when checking them in appropriate ways.51 Remarks about Super-Efficiency • The problem here is not due to irregularities of the density function, but due to the partialness of our estimator to µ0 = 0. • This example shows that no regularity conditions on the density can prevent an estimator from violating (3). This possibility can only be avoided by placing restrictions on the sequence of estimators. • LeCam (1953) showed that for any sequence of estimators satisfying (2), the set of points in Θ violating (3) has Lebesgue measure zero. • Superefficiency shows that “parametric” models can be useful and justified when checking them in appropriate ways