# Relation between asymptotic relative efficiency for tests and estimators

The asymptotic relative efficiency for unbiased estimators is the limit of the ratio of the variances as the $n\rightarrow \infty$. Is there a relation to asymptotic relative efficiency according to Pitman that looks at the limit of the number of data points required for specified power and significance level encyclopediaofmath.org?

• This would have to be for cases where the number of data points required for specified power is asymptotically proportional to variance. (This is typically the case.) For it to make sense to talk about "specified power" asymptotically, of course, we must be looking at some sequence of alternatives, not a fixed one. – Glen_b Jan 27 '15 at 1:59