TY - JOUR
T1 - Mean-risk tests of stochastic dominance
AU - Dentcheva, Darinka
AU - Stock, Gregory J.
AU - Rekeda, Ludmyla
N1 - Publisher Copyright:
© Oldenbourg Wissenschaftsverlag, München 2011.
PY - 2011/5/1
Y1 - 2011/5/1
N2 - We propose a new approach to testing whether one random variable is stochastically non-dominated by another one. The tests compare mean-risk differences of two unknown distributions using independent samples. The test can be used for comparison of the coherent risk measures of the distributions, as well as to reject stochastic dominance relation of first, second, or higher order between the two distributions. We consider several law-invariant coherent measures of risk which are consistent with the stochastic dominance relation of first and higher order. Numerical comparisons with the Mann-Whitney test and with the F-test for comparison of variance are provided. The numerical study indicates that most of the mean-risk tests are more powerful than the Mann-Whitney test.
AB - We propose a new approach to testing whether one random variable is stochastically non-dominated by another one. The tests compare mean-risk differences of two unknown distributions using independent samples. The test can be used for comparison of the coherent risk measures of the distributions, as well as to reject stochastic dominance relation of first, second, or higher order between the two distributions. We consider several law-invariant coherent measures of risk which are consistent with the stochastic dominance relation of first and higher order. Numerical comparisons with the Mann-Whitney test and with the F-test for comparison of variance are provided. The numerical study indicates that most of the mean-risk tests are more powerful than the Mann-Whitney test.
KW - Coherent measures of risk
KW - Mean-risk models
KW - Stochastic dominance efficiency
KW - Stochastic orders
UR - http://www.scopus.com/inward/record.url?scp=85024395759&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85024395759&partnerID=8YFLogxK
U2 - 10.1524/stnd.2011.1057
DO - 10.1524/stnd.2011.1057
M3 - Article
AN - SCOPUS:85024395759
SN - 2193-1402
VL - 28
SP - 97
EP - 118
JO - Statistics and Risk Modeling
JF - Statistics and Risk Modeling
IS - 2
ER -