Statistical Score Function

A Statistical Score Function is a score function that indicates how sensitively a likelihood function [math]\displaystyle{ L(\theta; X) }[/math] depends on its parameter [math]\displaystyle{ \theta }[/math].

• Context:
  • It can produce a Statistical Score.
• See: Statistical Inference, Test Statistic, Maximum Likelihood, Confidence Interval, Cramér–Rao Bound.

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References

2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Score_(statistics) Retrieved:2014-9-29.
  • In statistics, the score, score function, efficient score or informant indicates how sensitively a likelihood function [math]\displaystyle{ L(\theta; X) }[/math] depends on its parameter [math]\displaystyle{ \theta }[/math]. Explicitly, the score for [math]\displaystyle{ \theta }[/math] is the gradient of the log-likelihood with respect to [math]\displaystyle{ \theta }[/math]. 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.

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