M-Matrices as covariance matrices of multinormal distributions☆
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TLDR
The class of multivariate normal densities n (0, Σ ) whose inverse covariance matrix Σ −1 is an M-matrix is equivalent to this normal density being multivariate totally positive of order 2(MTP 2 ) as mentioned in this paper.About:
This article is published in Linear Algebra and its Applications.The article was published on 1983-07-01 and is currently open access. It has received 67 citations till now. The article focuses on the topics: Multivariate normal distribution & Estimation of covariance matrices.read more
Citations
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Conditional Association and Unidimensionality in Monotone Latent Variable Models
TL;DR: In this article, a broad class of latent variable models, namely the monotone unidimensional models, are studied, in which the latent variable is a scalar, the observable variables are conditionally independent given the Latent Variable, and the conditional distribution of the observables given the LSTM is stochastically increasing in the latent Variable.
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Estimation of positive definite M-matrices and structure learning for attractive Gaussian Markov Random fields
Martin Slawski,Matthias Hein +1 more
TL;DR: This work studies estimation of M-matrices taking the role of inverse second moment or precision matrices using sign-constrained log-determinant divergence minimization, and proposes an algorithm based on block coordinate descent in which each sub-problem can be recast as non-negative least squares problem.
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Introduction to Matrix Analysis. By Richard Bellman. 2nd Edition. Pp. xxiii, 403. £7·50. (McGraw-Hill.)
TL;DR: This book discusses Maximization, Minimization, and Motivation, which is concerned with the optimization of Symmetric Matrices, and its applications in Programming and Mathematical Economics.
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A characterization of monotone unidimensional latent variable models
Brian W. Junker,Jules L. Ellis +1 more
TL;DR: In this article, the authors generalize their work with a de Finetti-like characterization of the distribution of repeated measures that can be represented with mixtures of likelihoods of independent but not identically distributed random variables.
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Total positivity in Markov structures
Shaun M. Fallat,Steffen L. Lauritzen,Kayvan Sadeghi,Caroline Uhler,Nanny Wermuth,Piotr Zwiernik +5 more
TL;DR: In this paper, the authors discuss properties of distributions that are multivariate totally positive of order two (MTP2) related to conditional independence, and show that any independence model generated by an MTP2 distribution is a compositional semi-graphoid which is upward-stable and singletontransitive.
References
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Book
An Introduction to Multivariate Statistical Analysis
TL;DR: In this article, the distribution of the Mean Vector and the Covariance Matrix and the Generalized T2-Statistic is analyzed. But the distribution is not shown to be independent of sets of Variates.
Journal ArticleDOI
Introduction to Multivariate Statistical Analysis.
William G. Madow,T. W. Anderson +1 more
Book
Nonnegative Matrices in the Mathematical Sciences
TL;DR: 1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of non negative matrices 4. Symmetric nonnegativeMatrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative methods for linear systems 8. Finite Markov Chains
Book
Matrix iterative analysis
TL;DR: In this article, the authors propose Matrix Methods for Parabolic Partial Differential Equations (PPDE) and estimate of Acceleration Parameters, and derive the solution of Elliptic Difference Equations.