88 research outputs found
Current Open Questions in Complete Mixability
Complete and joint mixability has raised considerable interest in recent few
years, in both the theory of distributions with given margins, and applications
in discrete optimization and quantitative risk management. We list various open
questions in the theory of complete and joint mixability, which are
mathematically concrete, and yet accessible to a broad range of researchers
without specific background knowledge. In addition to the discussions on open
questions, some results contained in this paper are new
Nonparametric e-tests of symmetry
The notion of an e-value has been recently proposed as a possible alternative to critical regions and p-values in statistical hypothesis testing. In this paper we consider testing the nonparametric hypothesis of symmetry, introduce analogues for e-values of three popular nonparametric tests, define an analogue for e-values of Pitman's asymptotic relative efficiency, and apply it to the three nonparametric tests. We discuss limitations of our simple definition of asymptotic relative efficiency and list directions of further research
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