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 Scoring Algorithm  be random variables, independent and identically distributed with twice differentiable p.d.f. Scoring Algorithm , and we wish to calculate the maximum likelihood estimator (M.L.E.) Scoring Algorithm  of Scoring Algorithm . First, suppose we have a starting point for our algorithm Scoring Algorithm , and consider a Taylor expansion of the score function, Scoring Algorithm , about Scoring Algorithm :

    Scoring Algorithm 

where

    Scoring Algorithm 

is the observed information matrix at Scoring Algorithm . Now, setting Scoring Algorithm , using that Scoring Algorithm  and rearranging gives us:

    Scoring Algorithm 

We therefore use the algorithm

    Scoring Algorithm 

and under certain regularity conditions, it can be shown that Scoring Algorithm .

Fisher scoring

In practice, Scoring Algorithm  is usually replaced by Scoring Algorithm , the Fisher information, thus giving us the Fisher Scoring Algorithm:

    Scoring Algorithm ..

Under some regularity conditions, if Scoring Algorithm  is a consistent estimator, then Scoring Algorithm  (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.

See also

References

Further reading

Tags:

Scoring Algorithm Sketch of derivationScoring Algorithm Fisher scoringScoring Algorithm Further readingScoring AlgorithmMaximum likelihoodNewton's methodNumerical analysisRonald FisherStatistics

🔥 Trending searches on Wiki English:

2024 Summer OlympicsElizabeth YuArtificial intelligenceLeap yearHaussmann's renovation of ParisGermanyPhil McGrawJoey GraziadeiAdolf HitlerKristoffer OlssonTimothée ChalametMalcolm XKelly RowlandNicole KidmanNewcastle United F.C.Kate WinsletReal Madrid CFHottentot (racial term)Lauryn HillKillers of the Flower Moon (film)Tim KrulLondon StudioWilliam, Prince of Wales2024 Pakistani general electionLena (actress)Norman MorrisonThanksgiving (2023 film)My Chemical RomanceHarvey BarnesCheryl HinesMain PageThe Way (TV series)Barack ObamaUEFA Champions LeagueBattle of Moore's Creek BridgeHarry PotterM. Night ShyamalanJennifer GarnerHazbin HotelEurovision Song Contest 2024The Departed2024 Rajya Sabha electionsPatrick KaneHalo (TV series)Robin WilliamsU.S. stateBill GatesRun-DMCLondonOppenheimer (film)Ryan GarciaSweden–NATO relationsMarry My HusbandList of country calling codesTrue Detective (season 1)Yellowstone (American TV series)Ted LassoRobert De NiroBob MarleyLexi ThompsonWe Are the WorldJennifer Lopez2020 United States presidential electionWings HauserIlia TopuriaMinecraftFlaco (owl)Kara SwisherDavid BowieVultures 1Crew (film)Albert EinsteinBill SkarsgårdRule 34Tyler Perry🡆 More