Copulas with Prescribed Correlation Matrix

Abstract

Consider the convex set Rn of semi positive definite matrices of order n with diagonal \((1,\ldots,1).\) If μ is a distribution in \(\mathbb{R}^{n}\) with second moments, denote by R(μ) ∈ Rn its correlation matrix. Denote by Cn the set of distributions in [0, 1]n with all margins uniform on [0, 1] (called copulas). The paper proves that \(\mu \mapsto R(\mu )\) is a surjection from Cn on Rn if n ≤ 9. It also studies the Gaussian copulas μ such that R(μ) = R for a given R ∈ Rn. 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.School of Computer ScienceMcGill UniversityMontrealCanada
  2. 2.Equipe de Statistique et ProbabilitésUniversité de ToulouseToulouseFrance

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