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Fast procedure to compute empirical and Bernstein copulas

Author

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  • Hernández-Maldonado, Victor Miguel
  • Erdely, Arturo
  • Díaz-Viera, Martín
  • Rios, Leonardo

Abstract

In this work, a novel technique for efficient computation of bivariate empirical copulas and, by extension, non-parametrical copulas. The algorithm addresses discrete and finite equations, integrating mathematical-statistical components. It introduces two novel concepts: Propagation and Overlapping, to enhance computations and their comprehension during empirical copula construction. The algorithm is presented in pseudo-code for its implementation in any programming language. Comparative performance assessments demonstrate computing speeds ranging from 60 to 250 times faster than the standard algorithm across multiple case studies. Recent research highlights the utility of copulas in Artificial Intelligence (AI) techniques for enhanced predictions [8]. Existing studies center on parametric copulas, underscoring the significance of introducing a methodology for non-parametric copula implementation because this approach facilitates precise modeling of non-linear relationships among random variables, offering substantial improvements over conventional techniques, and boosting its integration, within the realm of artificial intelligence.

Suggested Citation

  • Hernández-Maldonado, Victor Miguel & Erdely, Arturo & Díaz-Viera, Martín & Rios, Leonardo, 2024. "Fast procedure to compute empirical and Bernstein copulas," Applied Mathematics and Computation, Elsevier, vol. 477(C).
    • Handle: RePEc:eee:apmaco:v:477:y:2024:i:c:s0096300324002881
    DOI: 10.1016/j.amc.2024.128827
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