Article Dans Une Revue Scandinavian Journal of Statistics Année : 2025

Dimension reduction for the estimation of the conditional tail-index

Résumé

We are interested in the relationship between the large values of a real random variable $Y$ and its associated covariate $X$, which takes values in a subset ${\cal{X}}$ of $\R^p$, when the conditional distribution of $Y$ given $X=x$ is heavy-tailed with a conditional tail-index $\gamma(x)>0$. Estimating this index is a critical step for inferring the conditional distribution, but the task becomes increasingly challenging as the dimension $p$ grows. The objective of this work is to propose a dimension reduction method to obtain a more efficient estimator of $\gamma(x)$. Specifically, we assume the existence of a subspace $\mathcal{S}_0$ of dimension $q

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Dates et versions

hal-04589742 , version 1 (27-05-2024)
hal-04589742 , version 2 (10-12-2024)
hal-04589742 , version 3 (05-05-2025)

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  • HAL Id : hal-04589742 , version 3

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Laurent Gardes, Alex Podgorny. Dimension reduction for the estimation of the conditional tail-index. Scandinavian Journal of Statistics, 2025, 52 (3), pp.1444--1476. ⟨hal-04589742v3⟩
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