Scoring algorithm
Scoring algorithm, also known as Fisher's scoring, is a form of Newton's method used in statistics to solve maximum likelihood equations numerically, named after Ronald Fisher.Sketch of derivation
Let be random variables, independent and identically distributed with twice differentiable p.d.f., and we wish to calculate the maximum likelihood estimator 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.Fisher scoring
In practice, is usually replaced by, the Fisher information, thus giving us the Fisher Scoring Algorithm:
