Transcription of Likelihood Ratio Tests - Missouri State University
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Likelihood Ratio Tests - Missouri State University
Math 541: Statistical Theory IILikelihood Ratio TestsInstructor: Songfeng ZhengA very popular form of hypothesis test is the Likelihood Ratio test, which is a generalization ofthe optimal test for simple null and alternative hypotheses that was developed by Neymanand Pearson (We skipped Neyman-Pearson lemma because we are short of time). Thelikelihood Ratio test is based on the Likelihood functionfn(X 1, , Xn| ), and the intuitionthat the Likelihood function tends to be highest near the true value of . Indeed, this is alsothe foundation for maximum Likelihood estimation.
distribution. We can look at the chi-square table under 10 degrees of freedom to flnd that 3.94 is the value under which there is 0.05 area. Using this, we can obtain P(2 2 P Xi • 3:94) = 0:05. This implies that we should reject the null hypothesis if P Xi • 3:94 in this example.
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