The natural vector bundle of the set of multivariate density functions
DOI:
https://doi.org/10.4067/S0716-09172005000300004Keywords:
Multivariate density function, Marginals, Vector bundle.Abstract
We find a description of the set of multivariate density functions with given marginals and introduce an associated vector bundle. The interest for the probability theory is restricted to the nonnegative elements in the sets of the derived vector bundle. The fiber is the space of all correlation measures among a multivariate density function and its unidimensional marginals.
References
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[13] Marchi, E. - Nucleolus, equilibria, correlation, Advances in Modeling & Simulation Modeling, Vol. 32, No. 2, pp. 7-11, (1996).
[14] Marchi, E. - On the possibility of an unusual extension of the minimax theorem, Z. Wahrsch. Verw. Geb., Vol. 12, pp. 224-270, (1969).
[15] Marchi, E. - Some topics on equilibria, Transactions of the American Mathematical Society, Vol. 220, No. 493, pp. 87-102, (1976).
[16] Marchi, E. - The natural vector bundle of the set of product probability, Z. Wahrsch. Verw. Geb., Vol. 23, pp. 7-17, (1972).
[17] Marchi, E. - Toward some steps in game theory, Japan Journal of Applied Math., Vol. 3, No. 2, pp. 343-355, (1986b).
[18] Marchi, E.: Una nota acerca de los puntos e-estables perfectos y propios, Collectanea Mathematica, Vol. 39, pp. 9-19, (1988).
[19] Morillas, P. M.: Nuevos tópicos en cópulas, funciones de densidad y un fibrado vectorial relacionado, Tesis doctoral, Universidad Nacional de San Luis, San Luis, Argentina, (2003).
[20] Nelsen, R. B.: An Introduction to Copulas, Lectures Notes in Statistics, Vol. 139, Springer-Verlag New York, Inc., (1999).
[21] Schweizer, B. - Thirty years of copulas, Advances in Probability Distributions with Given Marginals, Eds. G. DallAglio, S. Kotz, and G. Salinetti, Kluwer Academic Publishers, Dordrecht, pp. 13-50, (1991).
[22] Sklar, A. - Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris, Vol. 8, pp. 229-231, (1959).
[2] Cafarelli L. - The Monge-Ampére equation and optimal transportation, an elementary review, Lectures Notes in Mathematics, Vol. 1813, Springer-Verlag, pp. 1-10, (2003).
[3] DallAglio G. - Fréchet classes: the beginnings, Advances in Probability Distributions with Given Marginals, Eds. G. DallAglio, S. Kotz, and G. Salinetti. Kluwer Academic Publishers, Dordrecht, pp. 1-12, (1991).
[4] Fréchet, M. - Sur les tableaux de corrélation dont les marges sont données. Ann. Univ. Lyon, Sc., Vol. 4, pp. 53-84, (1951).
[5] Hoeffding, W. Masstabinvariante korrelationstheorie, Schriften des Matematischen Instituts und des Instituts für Angewandte Mathematik der Universität Berlin, Vol. 5, Heft 3, pp. 179-233, (1940).
[6] Hoeffding, W. - Masstabinvariante korrelationsmasse für diskontinuierliche Verteilungen, Arkiv für mathematischen Wirtschaften und Sozialforschung, Vol. 7, pp. 43-70, (1941).
[7] Joe, H. - Multivariate Models and Dependence Concepts, Chapman & Hall, London, (1997).
[8] Larotonda A. - Notas de Variedades Diferenciables, INMABB, Universidad Nacional de Bahía Blanca, Argentina, (1980).
[9] Landsburg S. - Nash equilibria in quantum games, preprint available at http://www.landsburg.com/pdf.
[10] Marchi, E., García Jurado I. and Prada J. M. - Refinamientos del concepto de equilibrio en extensiones generalizadas de juegos finitos, Investigación Operativa, Vol. 6, No. 1, pp. 83-92, (1991).
[11] Marchi, E. - Cooperative equilibrium, Compt. & Math. with Appl., Vol. 12B, No. 5/6, pp. 1185-1186, (1986a).
[12] Marchi, E. - Equilibrium points for rational games related with partitioned expanding economies, Advances in Modeling & Simulation, Vol. 32, No. 2, pp. 57-64, (1992).
[13] Marchi, E. - Nucleolus, equilibria, correlation, Advances in Modeling & Simulation Modeling, Vol. 32, No. 2, pp. 7-11, (1996).
[14] Marchi, E. - On the possibility of an unusual extension of the minimax theorem, Z. Wahrsch. Verw. Geb., Vol. 12, pp. 224-270, (1969).
[15] Marchi, E. - Some topics on equilibria, Transactions of the American Mathematical Society, Vol. 220, No. 493, pp. 87-102, (1976).
[16] Marchi, E. - The natural vector bundle of the set of product probability, Z. Wahrsch. Verw. Geb., Vol. 23, pp. 7-17, (1972).
[17] Marchi, E. - Toward some steps in game theory, Japan Journal of Applied Math., Vol. 3, No. 2, pp. 343-355, (1986b).
[18] Marchi, E.: Una nota acerca de los puntos e-estables perfectos y propios, Collectanea Mathematica, Vol. 39, pp. 9-19, (1988).
[19] Morillas, P. M.: Nuevos tópicos en cópulas, funciones de densidad y un fibrado vectorial relacionado, Tesis doctoral, Universidad Nacional de San Luis, San Luis, Argentina, (2003).
[20] Nelsen, R. B.: An Introduction to Copulas, Lectures Notes in Statistics, Vol. 139, Springer-Verlag New York, Inc., (1999).
[21] Schweizer, B. - Thirty years of copulas, Advances in Probability Distributions with Given Marginals, Eds. G. DallAglio, S. Kotz, and G. Salinetti, Kluwer Academic Publishers, Dordrecht, pp. 13-50, (1991).
[22] Sklar, A. - Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris, Vol. 8, pp. 229-231, (1959).
Published
2017-04-20
How to Cite
[1]
E. Marchi and P. M. Morillas, “The natural vector bundle of the set of multivariate density functions”, Proyecciones (Antofagasta, On line), vol. 24, no. 3, pp. 239-255, Apr. 2017.
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