Journal ArticleDOI
Maximum-likelihood estimates and likelihood-ratio criteria for multivariate elliptically contoured distributions
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For a class of multivariate elliptically contoured distributions, the maximum likelihood estimators of the mean vector and covariance matrix were found under certain conditions in this article, and the likelihood-ratio criteria were obtained for the same form as in the normal case.Abstract:
For a class of multivariate elliptically contoured distributions the maximum-likelihood estimators of the mean vector and covariance matrix are found under certain conditions. Likelihood-ratio criteria are obtained for a class of null hypotheses. These have the same form as in the normal case.read more
Citations
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Journal ArticleDOI
Statistical inference in elliptically contoured and related distributions
Kai-Tang Fang,T. W. Anderson +1 more
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Analysis of Covariance Structures under Elliptical Distributions
TL;DR: In this article, the adjustment of normal theory methods for the analysis of covariance structures to make them applicable under the class of elliptical distributions was examined, and it was shown that if the model satisfies a mild scale invariance condition and the data have an elliptical distribution, the asymptotic covariance matrix of sample covariances has a structure that results in the retention of many of the asmptotic properties of normal theories.
Journal ArticleDOI
Multivariate tests based on left-spherically distributed linear scores
TL;DR: In this article, a method for multivariate testing based on low-dimensional, data-dependent, linear scores is proposed, which reduces the dimensionality of observations and increases the stability of the solutions.
Journal ArticleDOI
A semi-parametric approach to risk management
TL;DR: In this article, a semi-parametric replacement for the multivariate normal involving normal variance is proposed, which allows a more accurate modelling of tails, together with various degrees of tail dependence, while the whole return distribution can be modelled.
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A general near-exact distribution theory for the most common likelihood ratio test statistics used in Multivariate Analysis
TL;DR: In this paper, it was shown that the exact distributions of the most common likelihood ratio test (l.r.t.) statistics, that is, the ones used to test the independence of several sets of variables, the equality of several variance-covariance matrices, sphericity, and the equality properties of several mean vectors, may be expressed as the distribution of the product of independent Beta random variables or the given number of independent random variables.
References
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Journal ArticleDOI
Spherical Matrix Distributions and a Multivariate Model
TL;DR: In this paper, the authors consider inference about the parameters of a multivariate linear model, in which the usual assumption of normality for the errors is replaced by a weaker assumption of spherical symmetry, and show that inference about means is identical with that appropriate under normality, being based on a matrix generalization of "studentization".
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Robustness of Multivariate Tests
TL;DR: In this paper, the authors give necessary and sufficient conditions for the null distribution of a test statistic to remain the same in the class of left $\mathscr{O}(n)$-invariant distributions, including elliptically symmetric distributions.
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Invariant Distributions Associated with Matrix Laws Under Structural Symmetry
D. R. Jensen,Irving John Good +1 more
TL;DR: In this article, a random matrix Y(n x m) is a real matrix in the space En x m of real matrices having location-scale parameters (0, Q) such that O belongs to a linear subspace X# of En m; the distribution Y(Y) exhibits a type of structural symmetry; and a certain transformation T (Y) is translation-invariant with respect to? and is invariant under changes of scale.