Asymptotic relative efficiency

The purpose of asymptotic relative efficiency is to compare two statistical procedures by comparing the sample sizes, n₁ and n₂, say, at which those procedures achieve some given measure of performance; the ratio n₂/n₁ is called the relative efficiency of procedure one with respect to procedure two. Finite-sample evaluations being difficult or impossible, a sequence of measures of performances requiring that those sample sizes go to infinity is generally considered. If those measures of performance are indexed by n, say, so that n₁ and n₂ take the form n₁(n) and n₂(n), the limit lim_n→∞n₂(n)/n₁(n), if it exists, is called the asymptotic relative efficiency of procedure one with respect to procedure two.