Statistical Theory and Methods
Published Online: 15 JAN 2013
Copyright © 2002 John Wiley & Sons, Ltd
Encyclopedia of Environmetrics
How to Cite
Hallin, M. 2013. Neyman-Pearson Lemma. Encyclopedia of Environmetrics. 4.
- Published Online: 15 JAN 2013
Named after Jerzy Neyman and Egon Pearson, who published the result in 1933 , 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.  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