Testing against second-order stochastic dominance of multiple distributions. (English) Zbl 1312.62023
Summary: Second-order stochastic dominance plays an important role in reliability and various branches of economics such as finance and decision-making under risk, and statistical testing for the stochastic dominance is often useful in practice. In this paper, we present a test of stochastic equality under the constraint of second-order stochastic dominance based on the theory of empirical processes. The asymptotic distribution of the test statistic is obtained, and a simple method to compute the critical value is derived. Simulation results and real data examples are presented to illustrate the proposed test method.
Keywords:
second-order stochastic dominance; asymptotic distribution; hypothesis testing; weak convergenceReferences:
[1] | DOI: 10.1198/jbes.2010.07224 · Zbl 1214.62048 · doi:10.1198/jbes.2010.07224 |
[2] | DOI: 10.1093/biomet/92.1.159 · Zbl 1068.62054 · doi:10.1093/biomet/92.1.159 |
[3] | DOI: 10.1214/aos/1176348125 · Zbl 0761.62038 · doi:10.1214/aos/1176348125 |
[4] | DOI: 10.1080/03610929308831123 · Zbl 0791.62049 · doi:10.1080/03610929308831123 |
[5] | DOI: 10.1016/S0165-1765(98)00102-5 · Zbl 0914.90052 · doi:10.1016/S0165-1765(98)00102-5 |
[6] | DOI: 10.1080/01621459.1965.10480858 · doi:10.1080/01621459.1965.10480858 |
[7] | DOI: 10.1002/9781118032985 · doi:10.1002/9781118032985 |
[8] | Karamata J., Publ. Math. Univ. Belgrade 1 pp 145– (1932) |
[9] | DOI: 10.1017/S0266466600008884 · doi:10.1017/S0266466600008884 |
[10] | Marshall A. W., Inequalities: Theory of Majorization and Its Applications (1979) · Zbl 0437.26007 |
[11] | DOI: 10.2307/2295819 · doi:10.2307/2295819 |
[12] | Rojo J., Statist. Sinica 13 pp 903– (2003) |
[13] | Russell W. R., Studies in Economics of Uncertainty (1989) |
[14] | DOI: 10.1016/S0167-7152(97)00116-8 · Zbl 0937.62047 · doi:10.1016/S0167-7152(97)00116-8 |
[15] | Talagrand M., Ann. Inst. H. Poincaré (B) Prob. Statist. 24 pp 307– (1988) |
[16] | DOI: 10.1017/CBO9780511802256 · doi:10.1017/CBO9780511802256 |
[17] | DOI: 10.1007/978-1-4757-2545-2 · doi:10.1007/978-1-4757-2545-2 |
[18] | DOI: 10.1080/01621459.1996.10476737 · doi:10.1080/01621459.1996.10476737 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.