Score (statistics)

Score (statistics)

In statistics, the score, score function, efficient score or informant indicates how sensitively a likelihood function depends on its parameter . Explicitly, the score for is the gradient of the log-likelihood with respect to .

The score plays an important role in several aspects of inference. For example:

• in formulating a test statistic for a locally most powerful test;
• in approximating the error in a maximum likelihood estimate;
• in demonstrating the asymptotic sufficiency of a maximum likelihood estimate;
• in the formulation of confidence intervals;
• in demonstrations of the Cramér–Rao inequality.

The score function also plays an important role in computational statistics, as it can play a part in the computation of maximum likelihood estimates.