Generalised Likelihood ratio test

the generalized likelihood ratio is

$$ LR = \frac{max_{\theta \in \Omega} L(\theta)}{max_{\theta \in \omega} L(\theta)}$$

the test of $$H_0$$ against $$H_1$$ uses a rejection region of the form $$\{ LR > c \}$$

in large samples the likelihood ratio test often coincides with standard tests