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José A. Díaz-garcía - One of the best experts on this subject based on the ideXlab platform.

  • Singular Matrix variate Birnbaum-Saunders distribution under elliptical models
    arXiv: Statistics Theory, 2019
    Co-Authors: José A. Díaz-garcía, Francisco J. Caro-lopera
    Abstract:

    This work sets the Matrix variate Birnbaum-Saunders theory in the context of Singular distributions and elliptical models. The so termed Singular Matrix variate generalised Birnbaum-Saunders distribution is obtained with respect the Hausdorff measure. Several basic properties and particular cases of this distribution are also derived.

  • Jacobians of Singular Matrix transformations: Extensions
    arXiv: Statistics Theory, 2012
    Co-Authors: José A. Díaz-garcía, Ramón Gutiérrez-sánchez
    Abstract:

    This article presents a unified approach to simultaneously compute the Jacobians of several Singular Matrix transformations in the real, complex, quaternion and octonion cases. Formally, these Jacobians are obtained for real normed division algebras with respect to the Hausdorff measure.

  • Doubly Noncentral Singular Matrix Variate Beta Distributions
    Journal of Statistical Theory and Practice, 2010
    Co-Authors: José A. Díaz-garcía, Ramón Gutiérrez-jáimez
    Abstract:

    Using Greenacre’s definition of the symmetrised density function, in this paper, we propose an alternative approach to find the corresponding nonsymmetrised density function of doubly noncentral Singular Matrix variate beta type I and II distributions. As particular cases we obtain the noncentral Singular Matrix variate beta type I and II distributions.

  • Singular random Matrix decompositions: distributions
    Journal of Multivariate Analysis, 2005
    Co-Authors: José A. Díaz-garcía, Graciela González-farías
    Abstract:

    Assuming that Y has a Singular Matrix variate elliptically contoured distribution with respect to the Hausdorff measure, the distributions of several matrices associated to QR, modified QR, SV and polar decompositions of Matrix Y are determined, for central and non-central, non-Singular and Singular cases, as well as their relationship to the Wishart and pseudo-Wishart generalized Singular and non-Singular distributions. Some of these results are also applied to two particular subfamilies of elliptical distributions, the Singular Matrix variate normal distribution and the Singular Matrix variate symmetric Pearson type VII distribution.

Ramón Gutiérrez-jáimez - One of the best experts on this subject based on the ideXlab platform.

T K Sarkar - One of the best experts on this subject based on the ideXlab platform.

  • On SVD for estimating generalized eigenvalues of Singular Matrix pencil in noise
    1991. IEEE International Sympoisum on Circuits and Systems, 1991
    Co-Authors: T K Sarkar
    Abstract:

    Several algorithms for estimating generalized eigenvalues (GEs) of Singular Matrix pencils perturbed by noise are reviewed. The Singular value decomposition (SVD) is explored as the common structure in three basic algorithms: direct Matrix pencil algorithm, Pro-ESPRIT, and TLS-ESPRIT. It is shown that several SVD-based steps inherent in those algorithms are equivalent to the first-order approximation. Also, Pro-ESPRIT and TLS-Pro-ESPRIT are shown to be equivalent, and TLS-ESPRIT and LS-ESPRIT are shown to be asymptotically equivalent to the first-order approximation. For the problem of estimating superimposed complex exponential signals, the state space algorithm is shown to be also equivalent to the previous Matrix pencil algorithms to the first-order approximation. The threshold phenomenon is illustrated by a simulation result based on a damped sinusoidal signal. An improved state space algorithm is found to be the most robust to noise.

  • On SVD for estimating generalized eigenvalues of Singular Matrix pencil in noise
    IEEE Transactions on Signal Processing, 1991
    Co-Authors: T K Sarkar
    Abstract:

    Several algorithms for estimating generalized eigenvalues (GEs) of Singular Matrix pencils perturbed by noise are reviewed. The Singular value decomposition (SVD) is explored as the common structure in the three basic algorithms: direct Matrix pencil algorithm, pro-ESPRIT, and TLS-ESPRIT. It is shown that several SVD-based steps inherent in the algorithms are equivalent to the first-order approximation. In particular, the Pro-ESPRIT and its variant TLS-Pro-ESPRIT are shown to be equivalent, and the TLS-ESPRIT and its earlier version LS-ESPRIT are shown to be asymptotically equivalent to the first-order approximation. For the problem of estimating superimposed complex exponential signals, the state-space algorithm is shown to be also equivalent to the previous Matrix pencil algorithms to the first-order approximation. The second-order perturbation and the threshold phenomenon are illustrated by simulation results based on a damped sinusoidal signal. An improved state-space algorithm is found to be the most robust to noise.

Serguei Naboko - One of the best experts on this subject based on the ideXlab platform.

Bilender P. Allahverdiev - One of the best experts on this subject based on the ideXlab platform.

  • Spectral Analysis of Singular Matrix-Valued Sturm–Liouville Operators
    Mediterranean Journal of Mathematics, 2019
    Co-Authors: Bilender P. Allahverdiev
    Abstract:

    In the Hilbert space \(L_{W}^{2}([a,b);E)\) (\(-\infty 0\)) a space of boundary values of the symmetric Singular Matrix-valued Sturm–Liouville operator with maximal deficiency indices (2N, 2N) (in limit-circle case at Singular end point b) is constructed. With the help of the boundary conditions at a and b, all maximal dissipative, maximal accumulative and self-adjoint extensions of such a symmetric operator are established. In particular, the maximal dissipative operators with separated boundary conditions, called ‘dissipative at a’ and ‘self-adjoint at b’ are investigated. A self-adjoint dilation of the dissipative operator is constructed and then its incoming and outgoing spectral representations are determined. This representation allows us to determine the scattering Matrix of the dilation with the help of the Weyl Matrix-valued function of a self-adjoint Matrix-valued Sturm–Liouville operator. Further a functional model of the dissipative operator is determined and its characteristic function in terms of the scattering Matrix of the dilation (or of the Weyl function) is established. Finally, a theorem on completeness of the system of root vectors of the dissipative operator is proved.

  • Spectral Analysis of Singular Matrix-Valued Sturm–Liouville Operators
    Mediterranean Journal of Mathematics, 2019
    Co-Authors: Bilender P. Allahverdiev
    Abstract:

    In the Hilbert space $$L_{W}^{2}([a,b);E)$$ L W 2 ( [ a , b ) ; E ) ( $$-\infty

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