Score test

Rao's score test, or the score test (often known as the Lagrange multiplier test in econometrics) is a statistical test of a simple null hypothesis that a parameter of interest ${\displaystyle \theta }$ is equal to some particular value ${\displaystyle \theta _{0}}$. It is the most powerful test when the true value of ${\displaystyle \theta }$ is close to ${\displaystyle \theta _{0}}$. The main advantage of the score test is that it does not require an estimate of the information under the alternative hypothesis or unconstrained maximum likelihood. This constitutes a potential advantage in comparison to other tests, such as the Wald test and the generalized likelihood ratio test (GLRT). This makes testing feasible when the unconstrained maximum likelihood estimate is a boundary point in the parameter space.

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