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# Testing for Second-Order Stochastic Dominance of Two Distributions

Amarjot Kaur, B. L. S. Prakasa Rao and Harshinder Singh
Econometric Theory
Vol. 10, No. 5 (Dec., 1994), pp. 849-866
Stable URL: http://www.jstor.org/stable/3532856
Page Count: 18
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## Abstract

A distribution function F is said to stochastically dominate another distribution function G in the second-order sense if ∫-∞ xF(u)du≤ ∫-∞ xG(u)du, for all x. Second-order stochastic dominance plays an important role in economics, finance, and accounting. Here a statistical test has been constructed to test H0: ∫-∞ xF(u)du≤ ∫-∞ xG(u)du, for some x ∈ [a, b], against the hypothesis $H_{1}\colon \int_{-\infty}^{x}F(u)du>\int_{-\infty}^{x}G(u)du$, for all x ∈ [a, b], where a and b are any two real numbers. The test has been shown to be consistent and has an upper bound α on the asymptotic size. The test is expected to have usefulness for comparison of random prospects for risk averters.

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