Nonparametric multi-samples test for simple stochastic ordering against unrestricted alternative

Abstract

Statistical inferences under simple stochastic ordering for two continuous populations has a long and rich history. But further study for multiple populations is still expected. In this article, we consider $k(\ge 2)$ samples test for simple stochastic ordering against unrestricted alternative. A test statistic is constructed with the empirical distribution functions and the isotonic regression estimates of distribution functions, and the null asymptotic distribution of the proposed test statistic is given. A bootstrap procedure is suggested for the critical values, and some simulation results are presented to illustrate the proposed test method.

Keywords:

• Simple stochastic ordering
• isotonic regression estimator
• bootstrap critical values
• multi-samples test

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E15
• 62H10

Additional information

Funding

The research work of the first author is supported by grants from the Funding Project of National Natural Science (31872847), Funding Project of Science and Technology Research Plan of Weifang City (201301019), Doctoral Funding of Weifang (2016BS11). The work of the second author is partially supported by NSFC with No. 11771032.