Concept

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. 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.

Official source

https://en.wikipedia.org/wiki/Scoring_algorithm

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Myrto Limnios

Teaching & PhD Courses Empirical processes MATH-522 We learn how to control the nonasymptotic and random behavior of collections of estimators, when indexed by classes of functions/sets. Examples range from prototypical estimators used by statisticians, to nonparametric models used in machine learning. Regression methods MATH-408 General graduate course on regression methods

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