Neyman–Pearson Lemma
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J. Neyman and E.S. Pearson showed in 1933 that, in testing a simple null hypothesis against a simple alternative, the most powerful test is based on the likelihood ratio. Extensions to other situations, and the connection with statistical decision theory, are briefly described.
Keywords:
critical region;
power;
likelihood ratio;
unbiased test;
decision theory
[1] E. S. Pearson,et al. On the Problem of the Most Efficient Tests of Statistical Hypotheses , 1933 .
[2] P. J. Huber,et al. Minimax Tests and the Neyman-Pearson Lemma for Capacities , 1973 .
[3] Jerzy Neyman,et al. The testing of statistical hypotheses in relation to probabilities a priori , 1933, Mathematical Proceedings of the Cambridge Philosophical Society.