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Throughout this article, boldfaced unsubscripted and are used to refer to random vectors, and Roman subscripted and are used to refer to scalar random variables.. If the entries in the column vector = (,, …,) are random variables, each with finite variance and expected value, then the covariance matrix is the matrix whose (,) entry is the covariance [1]: 177 ...
The Fisher information matrix is used to calculate the covariance matrices associated with maximum-likelihood estimates. It can also be used in the formulation of test statistics, such as the Wald test. In Bayesian statistics, the Fisher information plays a role in the derivation of non-informative prior distributions according to Jeffreys ...
The Marchenko–Pastur distribution is important in the theory of random matrices. The bounded quantile-parameterized distributions , which are highly shape-flexible and can be parameterized with data using linear least squares (see Quantile-parameterized distribution#Transformations )
A matrix whose entries are all either 0 or 1. Synonym for (0,1)-matrix or logical matrix. [1] Bisymmetric matrix: A square matrix that is symmetric with respect to its main diagonal and its main cross-diagonal. Block-diagonal matrix: A block matrix with entries only on the diagonal. Block matrix: A matrix partitioned in sub-matrices called blocks.
The main problem is that when the true values of the dispersion matrix are unknown, then under the null hypothesis the probability of rejecting via a test depends on the unknown dispersion matrices. [1] In practice, this dependency harms inference when the dispersion matrices are far from each other or when the sample size is not large enough ...
[1] [2] [3] Exponential dispersion models play an important role in statistical theory, in particular in generalized linear models because they have a special structure which enables deductions to be made about appropriate statistical inference.