Journal: Journal of Multivariate Analysis

Abbreviation

J. Multivar. Anal.

Publisher

Elsevier

Journal Volumes

ISSN

1095-7243
0047-259X

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Publications1 - 10 of 17
  • Bounds for functions of multivariate risks
    Item type: Journal Article
    Embrechts, Paul; Puccetti, Giovanni (2006)
    Journal of Multivariate Analysis
  • Clusters, outliers, and regression : : fixed point clusters
    Item type: Journal Article
    Hennig, Christian (2003)
    Journal of Multivariate Analysis
  • Parametric convergence rate of a non-parametric estimator in multivariate mixtures of power series distributions under conditional independence
    Item type: Journal Article
    Balabdaoui, Fadoua; Besdziek, Harald; Wang, Yong (2026)
    Journal of Multivariate Analysis
    The conditional independence assumption has recently appeared in a growing body of literature on the estimation of multivariate mixtures. We consider here conditionally independent multivariate mixtures of power series distributions with infinite support, to which belong Poisson, Geometric or Negative Binomial mixtures. We show that for all these mixtures, the non-parametric maximum likelihood estimator converges to the truth at the rate (ln(nd))1+d/2n−1/2 in the Hellinger distance, where n denotes the size of the observed sample and d represents the dimension of the mixture. Using this result, we then construct a new non-parametric estimator based on the maximum likelihood estimator that converges with the parametric rate n−1/2 in all ℓp-distances, for p≥1. These convergences rates are supported by simulations and the theory is illustrated using the famous Vélib dataset of the bike sharing system of Paris. We also introduce a testing procedure for whether the conditional independence assumption is satisfied for a given sample. This testing procedure is applied for several multivariate mixtures, with varying levels of dependence, and is thereby shown to distinguish well between conditionally independent and dependent mixtures. Finally, we use this testing procedure to investigate whether conditional independence holds for Vélib dataset.
  • Testing for spherical and elliptical symmetry
    Item type: Journal Article
    Albisetti, Isaia; Balabdaoui, Fadoua; Holzmann, Hajo (2020)
    Journal of Multivariate Analysis
    We construct new testing procedures for spherical and elliptical symmetry based on the characterization that a random vector X with finite mean has a spherical distribution if and only if E[u⊤X|v⊤X]=0 holds for any two perpendicular vectors u and v. Our test is based on the Kolmogorov–Smirnov statistic, and its rejection region is found via the spherically symmetric bootstrap. We show the consistency of the spherically symmetric bootstrap test using a general Donsker theorem which is of some independent interest. For the case of testing for elliptical symmetry, the Kolmogorov–Smirnov statistic has an asymptotic drift term due to the estimated location and scale parameters. Therefore, an additional standardization is required in the bootstrap procedure. In a simulation study, the size and the power properties of our tests are assessed for several distributions and the performance is compared to that of several competing procedures. © 2020 Elsevier Inc.
  • Densities of nested Archimedean copulas
    Item type: Journal Article
    Hofert, Marius; Pham, David (2013)
    Journal of Multivariate Analysis
  • Bounds for the sum of dependent risks having overlapping marginals
    Item type: Journal Article
    Embrechts, Paul; Puccetti, Giovanni (2010)
    Journal of Multivariate Analysis
    We describe several analytical and numerical procedures to obtain bounds on the distribution function of a sum of $\textit{n}$ dependent risks having fixed overlapping marginals. As an application, we produce bounds on quantile-based risk measures for portfolios of financial and actuarial interest.
  • Likelihood inference for Archimedean copulas in high dimensions under known margins
    Item type: Journal Article
    Hofert, Marius; Mächler, Martin; McNeil, Alexander J. (2012)
    Journal of Multivariate Analysis
  • Heterogeneous tail generalized COMFORT modeling via Cholesky decomposition
    Item type: Journal Article
    Näf, Jeffrey; Paolella, Marc; Polak, Paweł (2019)
    Journal of Multivariate Analysis
  • Meta densities and the shape of their sample clouds
    Item type: Journal Article
    Balkema, August A.; Embrechts, Paul; Nolde, Natalia (2010)
    Journal of Multivariate Analysis
  • Worst possible sub-directions in high-dimensional models
    Item type: Journal Article
    van de Geer, Sara (2016)
    Journal of Multivariate Analysis
Publications1 - 10 of 17