On the relation between extremal dependence and concomitants

TL;DR

This paper explores how extremal dependence affects the behavior of maxima in concomitant-based sampling, revealing the influence of distribution transformations on limit degeneracy, with implications for statistical modeling and sampling efficiency.

Contribution

It investigates the impact of extremal dependence on the asymptotic behavior of maxima in concomitant approaches, providing new insights into distribution transformations and limit degeneracy.

Findings

Extremal dependence influences the asymptotic behavior of maxima.

Transformations of marginal distributions affect limit degeneracy.

Results inform the design of more effective sampling procedures.

Abstract

The study of concomitants has recently met a renewed interest due to its applications in selection procedures. For instance, concomitants are used in ranked-set sampling, to achieve efficiency and reduce cost when compared to the simple random sampling. In parallel, the search for new methods to provide a rich description of extremal dependence among multiple time series has rapidly grown, due also to its numerous practical implications and the lack of suitable models to assess it. Here, our aim is to investigate extremal dependence when choosing the concomitants approach. In this study, we show how the extremal dependence of a vector $(X, Y)$ impacts the asymptotic behavior of the maxima over subsets of concomitants. Furthermore, discussing the various conditions and results, we investigate how transformations of the marginal distributions of $X$ and $Y$ influence the degeneracy of the limit.