Semi-parametric approximation of Kendall’s distribution function and multivariate Return Periods
[Approximation semi-paramétrique de la fonction de distribution de Kendall et périodes de retour multivariées]
Journal de la société française de statistique, Numéro spécial sur les copules, Tome 154 (2013) no. 1, pp. 151-173.

Dans le cas bivarié, une approximation de la fonction de distribution de Kendall ainsi que de la période de retour de Kendall sont proposées. Le contexte théorique est celui de la théorie des copules. L’approche semi-paramétrique suggérée consiste à approcher la fonction de distribution de Kendall empirique par une fonction linéaire par morceaux sur l’intervalle unité. La robustesse de l’approche proposée est étudiée empiriquement par le biais de simulations.

In this work we outline a constructive approach for the approximation of Kendall’s distribution function and Kendall’s Return Period in the bivariate case. First, we introduce a suitable theoretical framework, based on the Theory of Copulas, where to embed the issue. Then, we outline an original construction procedure to approximate the empirical Kendall distribution function estimated using the available data. The whole approach is semi-parametric: the empirical Kendall distribution function is approximated via a (suitable) continuous piece-wise linear function on the unit interval. A sensitivity analysis is carried out via a simulation procedure, in order to investigate the robustness of the approach proposed against several relevant factors.

Keywords: Kendall’s distribution function, multivariate return periods, copulas, risk assessment
Mot clés : fonction de distribution de Kendall, périodes de retour multivariés, copules, évaluation de risque 
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Salvadori, Gianfausto; Durante, Fabrizio; Perrone, Elisa. Semi-parametric approximation of Kendall’s distribution function and multivariate Return Periods. Journal de la société française de statistique, Numéro spécial sur les copules, Tome 154 (2013) no. 1, pp. 151-173. http://www.numdam.org/item/JSFS_2013__154_1_151_0/

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