The most efficient possible estimator of a parameter was described as being absolutely efficient.

For estimators whose variance could be estimated using s/n, or some equivalent, the ratio of their variances provided an alternate measure in terms of the relative number of observations required to obtain a given variance. But, since this comparison is biased for small sample sizes, it was assumed that n approached infinity - and it became known as the asymptotic relative efficiency (or A.R.E.).