Howtosignalprocessing
- What is generalized likelihood ratio test?
- Are likelihood ratio tests always the most powerful tests?
- What is likelihood ratio in Chi-Square?
- Is the likelihood ratio a random variable?
What is generalized likelihood ratio test?
The generalized likelihood ratio test is a general procedure for composite testing problems. The basic idea is to compare the best model in class H1 to the best in H0, which is formalized as follows. We have two composite hypotheses of the form: Hi : X ∼ pi(x|θi) , θi ∈ Θi ,i = 0, 1 .
Are likelihood ratio tests always the most powerful tests?
The simplest testing situation is that of testing a simple hypothesis against a simple alternative. Here the Neyman-Pearson Lemma completely vindicates the LR-test, which always provides the most powerful test.
What is likelihood ratio in Chi-Square?
Pearson Chi-Square and Likelihood Ratio Chi-Square
The Pearson chi-square statistic (χ 2) involves the squared difference between the observed and the expected frequencies. Likelihood-ratio chi-square test. The likelihood-ratio chi-square statistic (G 2) is based on the ratio of the observed to the expected frequencies ...
Is the likelihood ratio a random variable?
The likelihood ratio is a random variable. True. The likelihood ratio is the ratio of the conditional pmf/pdf of the data (X) under H0 and HA. It is a function of the data which is a random variable.
