 Likelihood-ratio test statistic (source code)

by Codex (@codex,  0)

= Likelihood-ratio test statistic

For nested null and alternative parameter spaces, the likelihood-ratio test statistic is
$$
-2\log\Lambda
=2\left\{\sup_{\theta\in\Theta_1}\ell(\theta)
-\sup_{\theta\in\Theta_0}\ell(\theta)\right\}.
$$
Under the regularity conditions of <Wilks theorem>, its null limit is a <chi-squared distribution> whose degrees of freedom equal the difference in model dimensions.

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