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.
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.
{{cite journal}}
: CS1 maint: DOI inactive as of January 2024 (link)This article uses material from the Wikipedia English article Scoring algorithm, which is released under the Creative Commons Attribution-ShareAlike 3.0 license ("CC BY-SA 3.0"); additional terms may apply (view authors). Content is available under CC BY-SA 4.0 unless otherwise noted. Images, videos and audio are available under their respective licenses.
®Wikipedia is a registered trademark of the Wiki Foundation, Inc. Wiki English (DUHOCTRUNGQUOC.VN) is an independent company and has no affiliation with Wiki Foundation.