Autore
Borroni, Claudio Giovanni

Titolo
Mutual association measures
Periodico
Statistical methods & applications : Journal of the Italian Statistical Society
Anno: 2019 - Volume: 28 - Fascicolo: 4 - Pagina iniziale: 571 - Pagina finale: 591

Given two continuous variablesXandYwith copulaC,many attempts were madein the literature to provide a suitable representation of the set of all concordance mea-sures of the couple(X,Y), as defined by some axioms. Some papers concentratedon the need to let such measures vanish not only at independence but, more gener-ally, at indifference, i.e. in lack of any dominance of concordance or discordance in(X,Y).The concept of indifference (or reflection-invariance in the language of copu-las) led eventually to full characterizations of some well-defined subsets of measures.However, the built classes failed to contain some known measures, which cannot beregarded as averaged “distances” ofCfrom given reference copulas (markedly, theFrechét–Hoeffding bounds). This paper, then, proposes a method to enlarge the rep-resentation of concordance measures, so as to include such elements, denoted hereas mutual, which arise from averaged multiple comparisons of the copulaCitself.Mutual measures, like Kendall’s tau and a recent proposal based on mutual variability,depend on the choice of a generator function, which needs some assumptions listedhere. After defining some natural estimators for the elements of the enlarged class, theassumptions made on the generator are shown to guarantee that those statistics pos-sess desirable sample properties, such as asymptotic normality under independence.Distributions under contiguous alternatives and relative efficiencies, in addition, arederived under mild assumptions on the copula. The paper provides several examples,giving further insight to some comparisons formerly conducted in the literature onlyvia simulation.



SICI: 1618-2510(2019)28:4<571:MAM>2.0.ZU;2-M

Esportazione dati in Refworks (solo per utenti abilitati)

Biblioteche ACNP che possiedono il periodico