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# Jarad niemi ucsb n p lemma and lrts 28 may 2010 9 11

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Jarad Niemi (UCSB) N-P Lemma and LRTs 28 May 2010 9 / 11

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Likelihood ratio tests Definition Definition Define λ by λ = max θ Θ 0 L ( θ ) max θ Θ L ( θ ) where Θ = Θ 0 Θ a . A likelihood ratio test of H 0 : θ Θ 0 versus H a : θ Θ a employs λ as a test statistic, and the rejection region is determined by λ k . Theorem If Y 1 , . . . , Y n have joint likelihood function L ( θ ) . Let r 0 denote the number of free parameters specified by H 0 : θ Θ 0 and let r denote the number of free parameters specified by the statement θ Θ . Then, for large n, - 2 log( λ ) has approximately a χ 2 r - r 0 distribution. Jarad Niemi (UCSB) N-P Lemma and LRTs 28 May 2010 10 / 11
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• Spring '09
• Bennett
• Statistics, Probability, Null hypothesis, Hypothesis testing, Statistical hypothesis testing, Type I and type II errors, Likelihood-ratio test, Jarad Niemi

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