Neyman-Pearson lemma

English

Etymology

Named after Jerzy Neyman and Egon Pearson.

Proper noun

1. Template:Lb 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 $\mathrm{\Lambda }(x)=\frac{L({\theta }_0\mid x)}{L({\theta }_1\mid x)}\le \eta$ where $P(\mathrm{\Lambda }(X)\le \eta \mid H_0)=\alpha$ is the most powerful test of size α for a threshold η.