Functions of Singular Random Matrices with Applications

• Autores: José Antonio Díaz García, Ramón Gutiérrez Jáimez
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 14, Nº. 2, 2005, págs. 475-488
• Idioma: inglés
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• Resumen

  • This article describes how the Jacobian is found for certain functions of a singular random matrix, both in the general case and in that of a non-negative definite random matrix. The Jacobian of the transformation V = S2 is found when S is non-negative definite; in addition, the Jacobian of the transformation Y = X+ is determined when X+ is the generalized, or Moore-Penrose, inverse of X. Expressions for the densities of the generalized inverse of the central beta and F singular random matrices are proposed. Finally, two applications in the field of Bayesian inference are presented.