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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