Neyman-Pearson lemma

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 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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Meanings

proper noun
  1. mathematicsA 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.

Origin

Named after Jerzy Neyman and Egon Pearson.

Full word history & related roots →
Cite this entry
APA

Neyman-Pearson lemma. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Neyman-Pearson%20lemma

MLA

“Neyman-Pearson lemma.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Neyman-Pearson%20lemma. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Neyman-Pearson lemma,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Neyman-Pearson%20lemma.

Source: Neyman-Pearson lemma on Wiktionary, CC BY-SA 4.0.