I need help with a Statistics question. All explanations and answers will be used to help me learn.
What is the likelihood ratio test? When can you use likelihood ratio test? What is a generalized likelihood ratio test? What is the difference between generalized likelihood ratio test and likelihood ratio test?
for example
1
The likelihood ratio test is the test that uses the ratio of the likelihood functions to find a good test statistic, an example of this is the most powerful test. The likelihood ratio test is used for simple hypotheses.
A generalized likelihood ratio test is used for none simple hypotheses, unlike the likelihood ratio test. The generalized likelihood ratio test uses the ratio of the maximum likelihood to find the test statistic.
2
The likelihood ratio test gives you a good test statistic by taking the ratio of the likelihood of H_a (alternative hypothesis) to the likelihood of H_0 (null hypothesis). The likelihood ratio test can only be used when testing between 2 simple hypotheses, it doesn’t work for composite hypotheses.
The two tests are similar in that they can both can be used to find good test statistics, but the difference is that the LR test is used for simple hypotheses while the GLR test is used to test composite hypotheses.
3
The likelihood ratio test is a test that compares the likelihood functions of the alternative hypothesis and null hypothesis to find the best test statistic. You can only use the likelihood ratio test with simple hypotheses.
The generalized likelihood ratio test is similar to the likelihood ratio test but use the maximum likelihood functions of the hypotheses. The difference between the two is that the GLRT works for composite hypotheses while LRT only works for simple hypotheses.
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