A symptotic R elative E fficiency: Theory

Abstract

Abstract The purpose of asymptotic relative efficiency is to compare two statistical procedures by comparing the sample sizes, n 1 and n 2 , say, at which those procedures achieve some given measure of performance; the ratio n 2 / n 1 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 n 1 and n 2 take the form n 1 ( n ) and n 2 ( n ), the limit lim n →∞ n 2 ( n )/ n 1 ( n ), if it exists, is called the asymptotic relative efficiency of procedure one with respect to procedure two.