Superefficient estimator

hyperefficient estimator

An abbreviation of the phrase "superefficient sequence of estimators" , used for a consistent sequence of asymptotically-normal estimators of an unknown parameter that is better (more efficient) than a consistent sequence of maximum-likelihood estimators.

Let be independent identically-distributed random variables that take values in a sampling space , . Suppose that the family of distributions is such that there is a consistent sequence of maximum-likelihood estimators of the parameter . Let be a sequence of asymptotically-normal estimators of . If

for all , where is the Fisher amount of information, and if, in addition, the strict inequality

(*)

holds at least at one point , then the sequence is called superefficient relative to the quadratic loss function, and the points at which (*) holds are called points of superefficiency.

References

[1]	I.A. Ibragimov, R.Z. [R.Z. Khas'minskii] Has'minskii, "Statistical estimation: asymptotic theory" , Springer (1981) (Translated from Russian)
[2]	L. Schmetterer, "Introduction to mathematical statistics" , Springer (1974) (Translated from German)
[3]	L. le Cam, "On some asymptotic properties of maximum likelihood estimates and related Bayes estimates" Univ. California Publ. Stat. , 1 (1953) pp. 277–330