Scoring algorithm, also known as Fisher's scoring, [1] is a form of Newton's method used in statistics to solve maximum likelihood equations numerically, named after Ronald Fisher.
Let be random variables, independent and identically distributed with twice differentiable p.d.f. , and we wish to calculate the maximum likelihood estimator (M.L.E.) of . First, suppose we have a starting point for our algorithm , and consider a Taylor expansion of the score function, , about :
where
is the observed information matrix at . Now, setting , using that and rearranging gives us:
We therefore use the algorithm
and under certain regularity conditions, it can be shown that .
In practice, is usually replaced by , the Fisher information, thus giving us the Fisher Scoring Algorithm:
Under some regularity conditions, if is a consistent estimator, then (the correction after a single step) is 'optimal' in the sense that its error distribution is asymptotically identical to that of the true max-likelihood estimate. [2]
{{cite journal}}
: CS1 maint: DOI inactive as of July 2025 (link)