Séance Séminaire

Séminaire de Probabilités et Statistique

Extreme quantile regression: A coupling approach and Wasserstein distance

In this work, we develop two coupling approaches for extreme quantile regression. We consider i.i.d copies of Y, a real valued random variable, and X taking his values in R^d. We want an estimation of the conditional quantile of Y given X=x of order 1-a for a very small a >0.

We introduce the proportional tail model, strongly inspired by the heteroscedastic extremes developped by Einmahl, de Haan and Zhou. The main assumption is that the tail distribution of Y is asymptotically proportional to the conditional tail of Y given X=x. We propose and study estimators of both model parameters and conditional quantile, which are studied by coupling methods.

The first method is based on coupling of empirical processes while the second is related with optimal transport. Even if we establish the asymptotic normality of parameter estimators with both methods, the first is focused on the proper quantile estimation whereas the second is more focused on the estimation of the extreme value index in presence of bias and the elaboration of a validation procedure for our model.

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