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Positive Dependence of Signals

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Michel Denuit
Michel Denuit*
Affiliation:
Université Catholique de Louvain
*
∗Postal address: Institut de Statistique, Biostatistique & Sciences Actuarielles - ISBA, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium. Email address: michel.denuit@uclouvain.be
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Abstract

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In this paper we further investigate the problem considered by Mizuno (2006) in the special case of identically distributed signals. Specifically, we first propose an alternative sufficient condition of crossing type for the convex order to hold between the conditional expectations given signal. Then, we prove that the bivariate (2,1)-increasing convex order ensures that the conditional expectations are ordered in the convex sense. Finally, the L2 distance between the quantity of interest and its conditional expectation given signal (or expected conditional variance) is shown to decrease when the strength of the dependence increases (as measured by the (2,1)-increasing convex order).

Keywords

Concordance ordersupermodularityconvex orderconditional expectationbivariate order of increasing-convex type

MSC classification

Secondary: 60E15: Inequalities; stochastic orderings
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 3 , September 2010 , pp. 893 - 897
Copyright
Copyright © Applied Probability Trust 2010 

References

Denuit, M., Lefèvre, Cl. and Mesfioui, M. (1999). A class of bivariate stochastic orderings with applications in actuarial sciences. Insurance Math. Econom. 24, 31–50.CrossRefGoogle Scholar
Denuit, M., Lefèvre, Cl. and Shaked, M. (1998). The s-convex orders among real random variables, with applications. Math. Inequal. Appl. 1, 585–613.Google Scholar
Denuit, M., Dhaene, J., Goovaerts, M. J. and Kaas, R. (2005). Actuarial Theory for Dependent Risks: Measures, Orders and Models. John Wiley, New York CrossRefGoogle Scholar
Ganuza, J.-J. and Penalva, J. S. (2010). Signal orderings based on dispersion and the supply of private information in auctions. Econometrica 78, 1007–1030.Google Scholar
Mizuno, T. (2006). A relation between positive dependence of signal and variability of conditional expectation given signal. J. Appl. Prob. 43, 1181–1185.CrossRefGoogle Scholar
Muliere, P. and Petrone, S. (1992). Generalized Lorenz curve and monotone dependence orderings. Metron 50, 19–38.Google Scholar
Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York.CrossRefGoogle Scholar