  This study presents a simulation study to compare different non-parametric
global envelopes that are refinements of the rank envelope proposed by
Myllym\"aki et al. (2017, Global envelope tests for spatial processes, J. R.
Statist. Soc. B 79, 381-404, doi: 10.1111/rssb.12172). The global envelopes are
constructed for a set of functions or vectors. For a large number of vectors,
all the refinements lead to the same outcome as the global rank envelope. For
smaller numbers of vectors the refinement playes a role, where different
refinements are sensitive to different types of extremeness of a vector among
the set of vectors. The performance of the different alternatives are compared
in a simulation study with respect to the numbers of available vectors, the
dimensionality of the vectors, the amount of dependence between the vector
elements and the expected type of extremeness.
