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Fast inference in copula models with categorical explanatory variables using the one-step procedure

Author

Listed:
  • Alexandre Brouste

    (Le Mans Université, Laboratoire Manceau de Mathématiques)

  • Christophe Dutang

    (Université Grenoble Alpes, CNRS, Grenoble INP, LJK)

  • Lilit Hovsepyan

    (Le Mans Université, Laboratoire Manceau de Mathématiques)

  • Tom Rohmer

    (Université de Toulouse, INRAE, ENVT, GenPhySE)

Abstract

A fast calibration procedure is presented for multivariate regression models with categorical explanatory variables. The marginal distributions are modeled using generalized linear models (GLMs), and the dependency structure between coordinates is captured via a parametric copula, yielding a flexible and interpretable framework for multivariate analysis. While the inference functions for margins (IFM) method, based on a two-step estimation separating marginals and copula, offers practical simplification over full maximum likelihood estimation (MLE), it remains computationally intensive in high-dimensional settings involving numerous covariates, modalities, or large sample sizes. To overcome this limitation, a one-step estimator is introduced, relying on a closed-form initial guess previously developed for univariate GLMs with categorical covariates. Compared to both full MLE and classical IFM-MLE, the proposed method significantly reduces computation time while maintaining similar asymptotic variance. The approach is validated through a simulation analysis and an application to real-world insurance data.

Suggested Citation

  • Alexandre Brouste & Christophe Dutang & Lilit Hovsepyan & Tom Rohmer, 2026. "Fast inference in copula models with categorical explanatory variables using the one-step procedure," Computational Statistics, Springer, vol. 41(1), pages 1-30, January.
    • Handle: RePEc:spr:compst:v:41:y:2026:i:1:d:10.1007_s00180-025-01692-5
    DOI: 10.1007/s00180-025-01692-5
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    References listed on IDEAS

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    1. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    2. Li, Zhengxiao & Beirlant, Jan & Yang, Liang, 2022. "A new class of copula regression models for modelling multivariate heavy-tailed data," Insurance: Mathematics and Economics, Elsevier, vol. 104(C), pages 243-261.
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