Neyman-Pearson Lemma Definition

A lemma stating that when performing a hypothesis test between two point hypotheses H0: θ = θ0 and H1: θ = θ1, then the likelihood-ratio test which rejects H0 in favour of H1 when \Lambda(x)=\frac{ L( \theta _0 \mid x)}{ L (\theta _1 \mid x)} \leq \eta where P(\Lambda(X)\leq \eta\mid H_0)=\alpha is the most powerful test of size α for a threshold η.


Origin of Neyman-Pearson Lemma

  • Named after Jerzy Neyman and Egon Pearson.

    From Wiktionary

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