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Difference between revisions of "Neyman-Pearson lemma"

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A lemma asserting that in the problem of statistically testing a simple hypothesis <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066600/n0666001.png" /> against a simple alternative <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066600/n0666002.png" /> the [[Likelihood-ratio test|likelihood-ratio test]] is a [[Most-powerful test|most-powerful test]] among all statistical tests having one and the same given [[Significance level|significance level]]. It was proved by J. Neyman and E.S. Pearson [[#References|[1]]]. It is often called the fundamental lemma of mathematical statistics. See also [[Statistical hypotheses, verification of|Statistical hypotheses, verification of]].
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A lemma asserting that in the problem of statistically testing a simple hypothesis $H_0$ against a simple alternative $H_1$ the [[Likelihood-ratio test|likelihood-ratio test]] is a [[Most-powerful test|most-powerful test]] among all statistical tests having one and the same given [[Significance level|significance level]]. It was proved by J. Neyman and E.S. Pearson [[#References|[1]]]. It is often called the fundamental lemma of mathematical statistics. See also [[Statistical hypotheses, verification of|Statistical hypotheses, verification of]].
  
 
====References====
 
====References====
 
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  J. Neyman,  E.S. Pearson,  "On the problem of the most efficient tests of statistical hypotheses"  ''Philos. Trans. Roy. Soc. London Ser. A.'' , '''231'''  (1933)  pp. 289–337</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  E.L. Lehmann,  "Statistical hypotheses testing" , Wiley  (1978)</TD></TR></table>
 
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  J. Neyman,  E.S. Pearson,  "On the problem of the most efficient tests of statistical hypotheses"  ''Philos. Trans. Roy. Soc. London Ser. A.'' , '''231'''  (1933)  pp. 289–337</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  E.L. Lehmann,  "Statistical hypotheses testing" , Wiley  (1978)</TD></TR></table>

Revision as of 16:41, 15 April 2014

A lemma asserting that in the problem of statistically testing a simple hypothesis $H_0$ against a simple alternative $H_1$ the likelihood-ratio test is a most-powerful test among all statistical tests having one and the same given significance level. It was proved by J. Neyman and E.S. Pearson [1]. It is often called the fundamental lemma of mathematical statistics. See also Statistical hypotheses, verification of.

References

[1] J. Neyman, E.S. Pearson, "On the problem of the most efficient tests of statistical hypotheses" Philos. Trans. Roy. Soc. London Ser. A. , 231 (1933) pp. 289–337
[2] E.L. Lehmann, "Statistical hypotheses testing" , Wiley (1978)
How to Cite This Entry:
Neyman-Pearson lemma. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Neyman-Pearson_lemma&oldid=22845
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article