• Neyman-Pearson lemma

Neyman-Pearson lemma (suomeksi)

Määritelmät:

• (lb, en, statistics) A lemma stating that when performing a hypothesis test between two point hypotheses ''H''₀: ''θ'' = ''θ''₀ and ''H''₁: ''θ'' = ''θ''₁, then the likelihood-ratio test which rejects ''H''₀ in favour of ''H''₁ 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.