Formation matrix
Encyclopedia
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.
These matrices appear naturally in the asymptotic expansion
of the distribution of many statistics related to the likelihood ratio.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
and information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...
, the expected formation matrix of a likelihood function
Likelihood function
In statistics, a likelihood function is a function of the parameters of a statistical model, defined as follows: the likelihood of a set of parameter values given some observed outcomes is equal to the probability of those observed outcomes given those parameter values...
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
Peter McCullagh
Peter McCullagh is an Irish statistician, originally from Plumbridge, Northern Ireland. He attended Birmingham University and completed his Ph.D. at Imperial College London under Sir David Cox and Anthony Atkinson. He is currently the John D...
, the symbol
is used to denote the element of the i-th line and j-th column of the observed formation matrix.These matrices appear naturally in the asymptotic expansion
Asymptotic expansion
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,...
of the distribution of many statistics related to the likelihood ratio.