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Multivariate Markov Families of Copulas

Ludger Overbeck, Wolfgang M. Schmidt (2015)

Dependence Modeling

For the Markov property of a multivariate process, a necessary and suficient condition on the multidimensional copula of the finite-dimensional distributions is given. This establishes that the Markov property is solely a property of the copula, i.e., of the dependence structure. This extends results by Darsow et al. [11] from dimension one to the multivariate case. In addition to the one-dimensional case also the spatial copula between the different dimensions has to be taken into account. Examples...

Multivariate measures of concordance for copulas and their marginals

M. D. Taylor (2016)

Dependence Modeling

Building upon earlier work in which axioms were formulated for multivariate measures of concordance, we examine properties of such measures. In particular,we examine the relations between the measure of concordance of an n-copula and the measures of concordance of the copula’s marginals.

Multivariate multiple comparisons with a control in elliptical populations

Naoya Okamoto, Takashi Seo (2013)

Discussiones Mathematicae Probability and Statistics

The approximate upper percentile of Hotelling's T²-type statistic is derived in order to construct simultaneous confidence intervals for comparisons with a control under elliptical populations with unequal sample sizes. Accuracy and conservativeness of Bonferroni approximations are evaluated via a Monte Carlo simulation study. Finally, we explain the real data analysis using procedures derived in this paper.

Multivariate normal approximation using Stein’s method and Malliavin calculus

Ivan Nourdin, Giovanni Peccati, Anthony Réveillac (2010)

Annales de l'I.H.P. Probabilités et statistiques

We combine Stein’s method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of gaussian fields. Among several examples, we provide an application to a functional version of the Breuer–Major CLT for fields subordinated to a fractional brownian motion.

Musielak-Orlicz spaces and prediction problems

Kazimierz Urbanik (2004)

Banach Center Publications

By a harmonizable sequence of random variables we mean the sequence of Fourier coefficients of a random measure M: X ₙ ( M ) = ∫ 0 1 e 2 π n i s M ( d s ) (n = 0,±1,...) The paper deals with prediction problems for sequences Xₙ(M) for isotropic and atomless random measures M. The crucial result asserts that the space of all complex-valued M-integrable functions on the unit interval is a Musielak-Orlicz space. Hence it follows that the problem for Xₙ(M) (n = 0,±1,...) to be deterministic is in fact an extremal problem of Szegö’s type...

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