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Copula measures and Sklar's theorem in arbitrary dimensions

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  • Fred Espen Benth
  • Giulia Di Nunno
  • Dennis Schroers

Abstract

Although copulas are used and defined for various infinite‐dimensional objects (e.g., Gaussian processes and Markov processes), there is no prevalent notion of a copula that unifies these concepts. We propose a unified functional analytic framework, show how Sklar's theorem can be applied in certain examples of Banach spaces and provide a semiparametric estimation procedure for second‐order stochastic processes with underlying Gaussian copula.

Suggested Citation

  • Fred Espen Benth & Giulia Di Nunno & Dennis Schroers, 2022. "Copula measures and Sklar's theorem in arbitrary dimensions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1144-1183, September.
    • Handle: RePEc:bla:scjsta:v:49:y:2022:i:3:p:1144-1183
    DOI: 10.1111/sjos.12559
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