TY - JOUR
T1 - Chebyshev inequalities with law-invariant deviation measures
AU - Grechuk, Bogdan
AU - Molyboha, Anton
AU - Zabarankin, Michael
PY - 2010/1
Y1 - 2010/1
N2 - The consistency of law-invariant general deviation measures with concave ordering has been used to generalize the RaoBlackwell theorem and to develop an approach for reducing minimization of law-invariant deviation measures to minimization of the measures on subsets of undominated random variables with respect to concave ordering. This approach has been applied for constructing the Chebyshev and Kolmogorov inequalities with law-invariant deviation measuresin particular with mean absolute deviation, lower semideviation and conditional value-at-risk deviation. Additionally, an advantage of the Kolmogorov inequality with certain deviation measures has been illustrated in estimating the probability of the exchange rate of two currencies to be within specified bounds.
AB - The consistency of law-invariant general deviation measures with concave ordering has been used to generalize the RaoBlackwell theorem and to develop an approach for reducing minimization of law-invariant deviation measures to minimization of the measures on subsets of undominated random variables with respect to concave ordering. This approach has been applied for constructing the Chebyshev and Kolmogorov inequalities with law-invariant deviation measuresin particular with mean absolute deviation, lower semideviation and conditional value-at-risk deviation. Additionally, an advantage of the Kolmogorov inequality with certain deviation measures has been illustrated in estimating the probability of the exchange rate of two currencies to be within specified bounds.
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U2 - 10.1017/S0269964809990192
DO - 10.1017/S0269964809990192
M3 - Article
AN - SCOPUS:74949105137
SN - 0269-9648
VL - 24
SP - 145
EP - 170
JO - Probability in the Engineering and Informational Sciences
JF - Probability in the Engineering and Informational Sciences
IS - 1
ER -