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Statements

Subject Item

dbr:Formation_matrix

rdfs:label

Formation matrix

rdfs:comment

In statistics and information theory, the expected formation matrix of a likelihood function is the matrix inverse of the Fisher information matrix of , while the observed formation matrix of is the inverse of the observed information matrix of . These matrices appear naturally in the asymptotic expansion of the distribution of many statistics related to the likelihood ratio.

dcterms:subject

dbc:Information_theory dbc:Estimation_theory

dbo:wikiPageID

6843217

dbo:wikiPageRevisionID

784699837

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dbc:Estimation_theory dbr:Statistics dbc:Information_theory dbr:Observed_information_matrix dbr:Asymptotic_expansion dbr:Information_theory dbr:Fisher_information dbr:Likelihood_function dbr:Fisher_information_matrix dbr:Likelihood-ratio_test dbr:Information_Geometry dbr:Einstein_notation dbr:Covariance_and_contravariance_of_vectors dbr:Peter_McCullagh dbr:Ole_E._Barndorff-Nielsen dbr:Differential_geometry dbr:Shannon_entropy

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dbo:abstract

In statistics and information theory, the expected formation matrix of a likelihood function is the matrix inverse of the Fisher information matrix of , while the observed formation matrix of is the inverse of the observed information matrix of . Currently, no notation for dealing with formation matrices is widely used, but in books and articles by Ole E. Barndorff-Nielsen and Peter McCullagh, the symbol is used to denote the element of the i-th line and j-th column of the observed formation matrix. The geometric interpretation of the Fisher information matrix (metric) leads to a notation of following the notation of the (contravariant) metric tensor in differential geometry. The Fisher information metric is denoted by so that using Einstein notation we have . These matrices appear naturally in the asymptotic expansion of the distribution of many statistics related to the likelihood ratio.

prov:wasDerivedFrom

wikipedia-en:Formation_matrix?oldid=784699837&ns=0

dbo:wikiPageLength

1911

foaf:isPrimaryTopicOf

wikipedia-en:Formation_matrix