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Pré-Publication, Document De Travail Année : 2023

Estimation of extreme L1 -multivariate expectiles with functional covariates

Résumé

The present article is devoted to the semi-parametric estimation of multivariate expectiles for extreme levels. The considered multivariate risk measures also include the possible conditioning with respect to a functional covariate, belonging to an infinite-dimensional space. By using the first order optimality condition, we interpret these expectiles as solutions of a multidimensional nonlinear optimum problem. Then the inference is based on a minimization algorithm of gradient descent type, coupled with consistent kernel estimations of our key statistical quantities such as conditional quantiles, conditional tail index and conditional tail dependence functions. The method is valid for equivalently heavy-tailed marginals and under a multivariate regular variation condition on the underlying unknown random vector with arbitrary dependence structure. Our main result establishes the consistency in probability of the optimum approximated solution vectors with a speed rate. This allows us to estimate the global computational cost of the whole procedure according to the data sample size.
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Dates et versions

hal-04051376 , version 1 (29-03-2023)

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  • HAL Id : hal-04051376 , version 1

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Elena Di Bernardino, Thomas Laloë, Cambyse Pakzad. Estimation of extreme L1 -multivariate expectiles with functional covariates. 2023. ⟨hal-04051376⟩
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