Neyman-Pearson lemma

Meaning

Proper Noun

• 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 $\backslash Lambda(x)=\backslash frac\{\; L(\; \backslash theta\; \_0\; \backslash mid\; x)\}\{\; L\; (\backslash theta\; \_1\; \backslash mid\; x)\}\; \backslash leq\; \backslash eta$ where $P(\backslash Lambda(X)\backslash leq\; \backslash eta\backslash mid\; H\_0)=\backslash alpha$ is the most powerful test of size α for a threshold η.

Origin

• Named after Jerzy Neyman and Egon Pearson.