Score Test

Definition

the Score test Statistic for the hypothesis $H_0:\theta ={\theta }_0,H_1:\theta \ne {\theta }_0$ is given by ${\chi }_S^2={\left(\frac{l^{\prime }({\theta }_0)}{\sqrt{nI({\theta }_0)}}\right)}^2\stackrel{D}{\to }{\chi }^2(1)$