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Derivatives and Fisher information of bivariate copulas

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  • Ulf Schepsmeier
  • Jakob Stöber

Abstract

Data sets with complex relationships between random variables are increasingly studied in statistical applications. A popular approach to model their dependence is the use of copula functions. Our contribution is to derive expressions for the observed and expected information for several bivariate copula families, in particular for the Student’s $$t$$ -copula. Further likelihood derivatives which are required for numerical implementations are computed and a numerically stable implementation is provided in the R-package VineCopula. Using a real world data set of stock returns, we demonstrate the applicability of our approach for the routinely calculation of standard errors. In particular, we illustrate how this prevents overestimating the time-variation of dependence parameters in a rolling window analysis. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • Ulf Schepsmeier & Jakob Stöber, 2014. "Derivatives and Fisher information of bivariate copulas," Statistical Papers, Springer, vol. 55(2), pages 525-542, May.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:2:p:525-542
    DOI: 10.1007/s00362-013-0498-x
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    4. Nguyen, Hoang & Ausín, M. Concepción & Galeano, Pedro, 2020. "Variational inference for high dimensional structured factor copulas," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
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    7. Deresa, N.W. & Van Keilegom, I. & Antonio, K., 2022. "Copula-based inference for bivariate survival data with left truncation and dependent censoring," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 1-21.
    8. Matthieu Garcin & Maxime L. D. Nicolas, 2021. "Nonparametric estimator of the tail dependence coefficient: balancing bias and variance," Papers 2111.11128, arXiv.org, revised Jul 2023.
    9. Stöber, Jakob & Hong, Hyokyoung Grace & Czado, Claudia & Ghosh, Pulak, 2015. "Comorbidity of chronic diseases in the elderly: Patterns identified by a copula design for mixed responses," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 28-39.
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    12. Elizabeth D. Schifano & Himchan Jeong & Ved Deshpande & Dipak K. Dey, 2021. "Fully and empirical Bayes approaches to estimating copula-based models for bivariate mixed outcomes using Hamiltonian Monte Carlo," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 133-152, March.
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