Quantiles of the conditional residual lifetime

On M-estimators of Approximate Quantiles and Approximate Conditional Quantiles

M-estimators introduced in Huber (1964) provide a class of robust estimators of a center of symmetry of a symmetric probability distribution which also have very high eeciency at the model. However it is not clear what they do estimate when the probability distributions are nonsymmetric. In this paper we rst show that in the case of arbitrary, not necessarily symmetric probabilty distributions,...

Nonparametric Estimation of Extreme Conditional Quantiles

The estimation of extreme conditional quantiles is an important issue in different scientific disciplines. Up to now, the extreme value literature focused mainly on estimation procedures based on i.i.d. samples. On the other hand, quantile regression based procedures work well for estimation within the data range i.e. the estimation of nonextreme quantiles but break down when main interest is i...

Functional kernel estimators of large conditional quantiles

Functional kernel estimators of conditional extreme quantiles

We address the estimation of “extreme” conditional quantiles i.e. when their order converges to one as the sample size increases. Conditions on the rate of convergence of their order to one are provided to obtain asymptotically Gaussian distributed kernel estimators. A Weissman-type estimator and kernel estimators of the conditional tailindex are derived, permitting to estimate extreme conditio...

Functional nonparametric estimation of conditional extreme quantiles

− We address the estimation of quantiles from heavy-tailed distributions when functional covariate information is available and in the case where the order of the quantile converges to one as the sample size increases. Such ”extreme” quantiles can be located in the range of the data or near and even beyond the boundary of the sample, depending on the convergence rate of their order to one. Nonp...