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Asymptotic Relative Efficiency (ARE)

Statistical Theory and Methods

  1. Marc Hallin1,2

Published Online: 15 JAN 2013

DOI: 10.1002/9780470057339.vnn077

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Hallin, M. 2013. Asymptotic Relative Efficiency (ARE). Encyclopedia of Environmetrics. 1.

Author Information

  1. 1

    Université Libre de Bruxelles, Bruxelles, Belgium

  2. 2

    ORFE, Princeton University, Princeton, NJ, USA

Publication History

  1. Published Online: 15 JAN 2013

Abstract

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 limn[RIGHTWARDS ARROW]n2(n)/n1(n), if it exists, is called the asymptotic relative efficiency of procedure one with respect to procedure two.

Keywords:

  • point estimation;
  • hypothesis testing;
  • asymptotic efficiency;
  • Pitman efficiency;
  • Bahadur efficiency