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A relation between positive dependence of signal and the variability of conditional expectation given signal

Published online by Cambridge University Press:  14 July 2016

Toshihide Mizuno*
Affiliation:
University of Hyogo
*
Postal address: School of Economics, University of Hyogo, Gakuen-Nishi-Machi, Nishi-ku, Kobe, Hyogo, 651-2197, Japan. Email address: mizuno@econ.u-hyogo.ac.jp
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Abstract

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Let S 1 and S 2 be two signals of a random variable X, where G 1(s 1x) and G 2(s 2x) are their conditional distributions given X = x. If, for all s 1 and s 2, G 1(s 1x) - G 2(s 2x) changes sign at most once from negative to positive as x increases, then the conditional expectation of X given S 1 is greater than the conditional expectation of X given S 2 in the convex order, provided that both conditional expectations are increasing. The stochastic order of the sufficient condition is equivalent to the more stochastically increasing order when S 1 and S 2 have the same marginal distribution and, when S 1 and S 2 are sums of X and independent noises, it is equivalent to the dispersive order of the noises.

Information

Type
Short Communications
Copyright
© Applied Probability Trust 2006 

References

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