Nonparametric AMOC Changepoint Tests for Stochastically Ordered Alternatives

Abstract

The problem considered is that of testing on the basis of a finite sequence of independent observations if all the observations have the same distribution versus the alternative that there is a unique change in the distribution and i.i.d. observations after the change are stochastically larger. The distributions before and after the possible change are continuous but not fully specified. We suggest a family of nonparametric tests based on ranks. Asymptotic approximations for the significance level of the test are obtained analytically. Monte Carlo experiments show that the rate of convergence of our asymptotics is fast.

Keywords:

• AMOC procedure
• Change-point
• Mann-Whitney statistic
• Nonparametric statistics

Mathematics Subject Classification:

• 62G10
• 62G20
• 62G35

Acknowledgments

This work has benefited greatly from discussions with Professor Moshe Pollak and the author wishes to thank him for his very helpful comments and suggestions. The author is also indebted to the referees for their constructive suggestions that led to improvements in the article.