Difference between revisions of "Neyman-Pearson lemma"
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| − | A lemma asserting that in the problem of statistically testing a simple hypothesis | + | {{TEX|done}} |
| + | 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
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