Likelihood-ratio test | Wikipedia audio article
Channel: wikipedia tts
Date: 06/10/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Likelihood-ratio_test


00:00:51 1 Definition
00:01:17 1.1 General
00:03:01 1.2 Case of simple hypotheses
00:04:44 2 Interpretation
00:05:36 2.1 An example
00:06:54 3 Asymptotic distribution: Wilks’ theorem
00:07:46 4 See also



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SUMMARY
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In statistics, the likelihood-ratio test assesses the goodness of fit of two competing statistical models based on the ratio of their likelihoods, specifically one found by maximization over the entire parameter space and another found after imposing some constraint. If the constraint (i.e., the null hypothesis) is supported by the observed data, the two likelihoods should not differ by more than sampling error. Thus the likelihood-ratio test tests whether this ratio is significantly different from one, or equivalently whether its natural logarithm is significantly different from zero.
The likelihood-ratio test is the oldest of the three classical approaches to hypothesis testing, together with the Lagrange multiplier test and the Wald test. In fact, the latter two can be conceptualized as approximations to the likelihood-ratio test, and are asymptotically equivalent. In the case of comparing two models each of which has no unknown parameters, use of the likelihood-ratio test can be justified by the Neyman–Pearson lemma. The lemma demonstrates that the test has the highest power among all competitors.