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Neyman-Pearson Lemma

Statistical Theory and Methods

  1. Marc Hallin1,2

Published Online: 15 JAN 2013

DOI: 10.1002/9780470057339.vnn090

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Hallin, M. 2013. Neyman-Pearson Lemma. Encyclopedia of Environmetrics. 4.

Author Information

  1. 1

    ECARES, Université libre de Bruxelles, Bruxelles, Belgium

  2. 2

    Princeton University, Princeton, NJ, USA

Publication History

  1. Published Online: 15 JAN 2013


Named after Jerzy Neyman and Egon Pearson, who published the result in 1933 [1], the Neyman–Pearson lemma can be considered as the theoretical cornerstone of the modern theory of hypothesis testing. Although the situation it is addressing (a simple null hypothesis versus a simple alternative) is of limited practical value, this lemma paved the way for all further developments of the theory; see Ref. [2] for an overview. We briefly state that fundamental result, and describe some immediate applications to standard one-sided one-parameter problems.


  • hypothesis testing;
  • simple null versus simple alternative;
  • randomized test;
  • most powerful test;
  • uniformly most powerful test;
  • likelihood ratio test;
  • monotone likelihood ratio