Comparison of non-parametric global envelopes

TL;DR

This paper compares various non-parametric global envelope methods through simulation, highlighting how refinements perform differently based on the number of vectors and their dependence structure.

Contribution

It provides a comprehensive simulation-based comparison of non-parametric global envelope refinements, clarifying their performance under different conditions.

Findings

Refinements converge to the rank envelope with many vectors.

Different refinements are sensitive to different extremeness types.

Performance depends on vector number, dimensionality, and dependence.

Abstract

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.