Artículos científicos
Publicado 2013-12-17
Palabras clave
- Esperanza condicionada,
- independencia condicionada
Cómo citar
Marmolejo L., M. A., & Muñoz-Tello, A. F. (2013). Algunas propiedades de la independencia condicionada. Revista Integración, Temas De matemáticas, 31(2), 165–180. Recuperado a partir de https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/3755
Resumen
El objetivo de este artículo es el de establecer algunas propiedades nuevas de la independencia condicionada de una familia de clases de eventos. De una parte, se generalizan algunos de los resultados de Van Putten y Van Schuppen [15], que consideran el caso de una familia con dos elementos, y, de otra parte, se generalizan resultados conocidos sobre familias de clases de eventos independientes. Como aplicación, se dan algunas propiedades de la independencia condicionada de una familia de variables aleatorias.
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Referencias
[1] Ash R.B. and Dolèans-Dade C.A., Probability and Measure Theory, Second Edition, Academic Press, San Diego, 2000.
[2] Bauer H., Probability Theory, Walter de Guyter, New York, 1972.
[3] Basu D. and Pereira C.A.B., “Conditional independence in statistics”, Sankhy¯a Ser. A 45 (1983), no. 3, 324–337.
[4] Billingsley P., Probability and Measure, Jhon Wiley and Sons. Inc., New York, 1979.
[5] Grzenda W. and Zieba W., “Conditional Central Limit Theorems”, Int. Math. Forum 3 (2008), no. 31, 1521–1528.
[6] Jamison B., “Reciprocal processes: the stationary Gaussian case”, Ann. Math. Statist. 41 (1970), no. 5, 1624–1630.
[7] Loève M., Probability Theory II, Four Edition, Springer-Verlag, New York, 1978.
[8] Majerek D., Nowak W. and Zieba W., “Conditional Strong Law of Large Number”, Int. J. Pure and Appl. Math. 20 (2005), no. 2, 143–156.
[9] Majerek D. and Zieba W., “Conditional Martingales”, Acta Math. Vietnam. 32 (2007), no. 1, 41–50.
[10] Majerek D. and Zieba W., “Conditional Version of Marcinkiewicz-Zygmunt’s Theorem”, Int. Math. Forum 3 (2008), no. 25, 1233–1240.
[11] Nogales A.G. and Oyola J.A., “Some remarks on sufficiency, invariance and conditional independence”, Ann. Statist. 24 (1996), no. 2, 906–909.
[12] Nogales A.G., Oyola J.A. and Pérez P., “On conditional independence and the relationship between sufficience and invariance under the Bayesian point of view”, Statist. Probab. Lett. 46 (2000), no. 1, 75–84.
[13] Nualart D., The Malliavin Calculus and Related Topics, Springer-Verlag, New York, 1995.
[14] Prakasa Rao B.L.S., “Conditional independence, conditional mixing and conditional association”, Ann. Inst. Statist. Math. 61 (2009), no. 2, 441–460.
[15] Van Putten C. and Van Schuppen J.H., “Invariance properties of the conditional independence relation”, Ann. Probab. 13 (1985), no. 3, 934–945.
[16] Roussas G., “On conditional independence, mixing, and association”, Stoch. Anal. Appl. 26 (2008), no. 6, 1274–1309.
[17] Shiryaev A.N., Probability, Second Edition, Springer, New York, 1996.
[18] Williams D., Probability with Martingales, Cambridge University Press, Cambridge, 1997.
[2] Bauer H., Probability Theory, Walter de Guyter, New York, 1972.
[3] Basu D. and Pereira C.A.B., “Conditional independence in statistics”, Sankhy¯a Ser. A 45 (1983), no. 3, 324–337.
[4] Billingsley P., Probability and Measure, Jhon Wiley and Sons. Inc., New York, 1979.
[5] Grzenda W. and Zieba W., “Conditional Central Limit Theorems”, Int. Math. Forum 3 (2008), no. 31, 1521–1528.
[6] Jamison B., “Reciprocal processes: the stationary Gaussian case”, Ann. Math. Statist. 41 (1970), no. 5, 1624–1630.
[7] Loève M., Probability Theory II, Four Edition, Springer-Verlag, New York, 1978.
[8] Majerek D., Nowak W. and Zieba W., “Conditional Strong Law of Large Number”, Int. J. Pure and Appl. Math. 20 (2005), no. 2, 143–156.
[9] Majerek D. and Zieba W., “Conditional Martingales”, Acta Math. Vietnam. 32 (2007), no. 1, 41–50.
[10] Majerek D. and Zieba W., “Conditional Version of Marcinkiewicz-Zygmunt’s Theorem”, Int. Math. Forum 3 (2008), no. 25, 1233–1240.
[11] Nogales A.G. and Oyola J.A., “Some remarks on sufficiency, invariance and conditional independence”, Ann. Statist. 24 (1996), no. 2, 906–909.
[12] Nogales A.G., Oyola J.A. and Pérez P., “On conditional independence and the relationship between sufficience and invariance under the Bayesian point of view”, Statist. Probab. Lett. 46 (2000), no. 1, 75–84.
[13] Nualart D., The Malliavin Calculus and Related Topics, Springer-Verlag, New York, 1995.
[14] Prakasa Rao B.L.S., “Conditional independence, conditional mixing and conditional association”, Ann. Inst. Statist. Math. 61 (2009), no. 2, 441–460.
[15] Van Putten C. and Van Schuppen J.H., “Invariance properties of the conditional independence relation”, Ann. Probab. 13 (1985), no. 3, 934–945.
[16] Roussas G., “On conditional independence, mixing, and association”, Stoch. Anal. Appl. 26 (2008), no. 6, 1274–1309.
[17] Shiryaev A.N., Probability, Second Edition, Springer, New York, 1996.
[18] Williams D., Probability with Martingales, Cambridge University Press, Cambridge, 1997.