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This article has been tagged since September 2006. In statistics and information theory, the expected formation matrix of a likelihood function L(θ) is the matrix inverse of the Fisher information matrix of L(θ), while the observed formation matrix of L(θ) is the inverse of the observed information matrix of L(θ).
A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ...
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In statistics, a likelihood function is a conditional probability function considered a function of its second argument with its first argument held fixed, thus: and also any other function proportional to such a function. ...
In statistics, the Fisher information I(θ), thought of as the amount of information that an observable random variable carries about an unobservable parameter θ upon which the probability distribution of X depends, is the variance of the score. ...
Currently, no notation for dealing with formation matrices is widely used, but in Ole E. Barndorff-Nielsen and Peter McCullagh books and articles the simbol jij is used to denote de element of the i-th line and j-th column of the observed formation matrix.
These matrices appear naturally in the asymptotic expansion of the distribution of many statistics related to the likelihood ratio. In mathematics an asymptotic expansion, asymptotic series or Poincaré expansion is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation to a given function as the argument of the function tends towards a particular, often infinite, point. ...
A likelihood-ratio test is a statistical test relying on a test statistic computed by taking the ratio of the maximum value of the likelihood function under the constraint of the null hypothesis to the maximum with that constraint relaxed. ...
References
- Barndorff--Nielsen, O. and D.R. Cox, (1989), Asymptotic Techniques for Use in Statistics, Chapman and Hall, London.
- Barndorff-Nielsen, O.E. and Cox, D.R., (1994). Inference and Asymptotics. Chapman & Hall, London.
- P. McCullagh, "Tensor Methods in Statistics", Monographs on Statistics and Applied Probability, Chapman and Hall, 1987.
See also - Fisher information
- Shannon entropy
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