note that formula_24 is a function of formula_2 and the observation formula_8, so that, in general, it is not a statistic. however, in certain applications, such as the score test, the score is evaluated at a specific value of formula_2 (such as a null-hypothesis value), in which case the result is a statistic. intuitively, if the restricted estimator is near the maximum of the likelihood function, the score should not differ from zero by more than sampling error. in 1948, c. r. rao first proved that the square of the score divided by the information matrix follows an asymptotic χ-distribution under the null hypothesis.