Abstract. Wang & Wells [ J. Amer. Statist. Assoc. 95 (2000) 62] describe a non‐parametric approach for checking whether the dependence structure of random sample censored bivariate data is appropriately modelled by given family Archimedean copulas. Their procedure based on truncated version Kendall process introduced Genest Rivest 88 (1993) 1034] and later studied Barbe et al . Multivariate Anal. 58 (1996) 197]. Although determine asymptotic behaviour their process, model selection...

Pour tester qu’une loi P donnée provient d’une famille paramétrique $\mathcal{P}$, on est souvent amené à comparer une estimation non An fonctionnelle A de un élément Aθn correspondant θn θ. Dans bien des cas, la asymptotique statistiques tests bâties partir du processus n1/2(An−Aθn) dépend inconnue P. On montre ici que si les suites et d’estimateurs sont régulières dans sens précis, le recours au rééchantillonnage conduit approximations valides seuils tests. Autrement dit An* θn* analogues...

Continuation refers to the operation by which cumulative distribution function of a discontinuous random vector is made continuous through multilinear interpolation. The copula that results from application this technique classical empirical either called or checkerboard copula. As shown Genest and Ne\v{s}lehov\'{a} (Astin Bull. 37 (2007) 475-515) (J. Multivariate Anal. 98 544-567), plays central role in characterizing dependence concepts discrete vectors. In paper, authors establish...

The empirical checkerboard copula is a multilinear extension of the copula, which plays key role for inference in models. Weak convergence corresponding process based on random sample from underlying multivariate distribution established here under broad conditions allow arbitrary univariate margins. It only required that has continuous first-order partial derivatives an open subset unit hypercube. This assumption very weak and always satisfied when margins are discrete. When continuous, one...

A convergence theorem for martingales with càdlàg trajectories (right continuous left limits everywhere) is obtained in the sense of weak dual topology on Hilbert space, under conditions that are much weaker than those required any usual Skorohod topologies. Examples provided to show these also very easy check and yield useful asymptotic results, especially when limit a mixture stochastic processes discontinuities.

Deheuvels [J. Multivariate Anal. 11 (1981) 102–113] and Genest Rémillard [Test 13 (2004) 335–369] have shown that powerful rank tests of multivariate independence can be based on combinations asymptotically independent Cramér–von Mises statistics derived from a Möbius decomposition the empirical copula process. A result large-sample behavior this process under contiguous sequences alternatives is used here to give representation limiting distribution such test compute their relative local...

The asymptotic behaviour of the empirical copula constructed from residuals stochastic volatility models is studied. It shown that if matrix diagonal, then process behaves like parameters were known, a remarkable property. However, not true genuinely non-diagonal. Applications for goodness-of-fit and structural change dependence between innovations are discussed.

In this paper, we study the asymptotic behavior of sequential empirical process and copula process, both constructed from residuals multivariate stochastic volatility models. Applications for detection structural changes specification tests distribution innovations are discussed. It is also shown that if matrices diagonal, which case univariate time series estimated separately instead being jointly estimated, then behaves as were observed; a remarkable property. As by-product, one obtains...

Statistics are proposed for testing the hypothesis that arbitrary random variables mutually independent. The tests consistent and well behaved any marginal distributions; they can be used, example, contingency tables which sparse or whose dimension depends on sample size, as mixed data. No regularity conditions, data jittering, binning mechanisms required. statistics rank-based functionals of Cramér–von Mises type asymptotic behaviour derives from empirical multilinear copula process....