Neyman-Pearson Lemma

Theorem

The best critical region of size $\alpha$ for testing a simple null hypothesis $H_0$ against a simple alternative hypothesis $H_1$ based on a likelihood ratio is given by


This needs considerable tedious hard slog to complete it.
In particular: Nelson does not give details
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Proof


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Also see

  • Definition:Hypothesis Testing


Source of Name

This entry was named for Jerzy Neyman and Egon Sharpe Pearson‎.


Historical Note

The was the result of the work of Jerzy Neyman and Egon Sharpe Pearson‎ in $1937$.


Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Neyman-Pearson lemma
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Neyman-Pearson lemma
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