Last Updated
：2025/11/29
Neyman-Pearson lemma
Proper noun
Japanese Meaning
統計学において、2つの点仮説（帰無仮説 H₀: θ = θ₀ と対立仮説 H₁: θ = θ₁）の間で仮説検定を行う際、尤度比検定が有意水準αにおいて最も検出力の高い検定であることを示す補題。具体的には、尤度比 Λ(x) = L(θ₀|x) / L(θ₁|x) がある閾値η以下の場合に帰無仮説 H₀を棄却する検定が、指定されたα水準で最良の性能を持つことを述べている。
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(statistics) 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 𝛬(x)=(L(𝜃₀∣x))/(L(𝜃₁∣x))≤𝜂 where P(𝛬(X)≤𝜂∣H_0)=𝛼 is the most powerful test of size α for a threshold η.
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Neyman-Pearson lemma
When constructing tests for simple hypotheses, the Neyman-Pearson lemma shows that the likelihood-ratio test maximizes power among all tests with the same significance level.
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When constructing tests for simple hypotheses, the Neyman-Pearson lemma shows that the likelihood-ratio test maximizes power among all tests with the same significance level.
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