Functional kernel estimators of large conditional quantiles

By Laurent Gardes, Stéphane Girard. 2011

56 citations recorded by the source corpus.

We address the estimation of conditional quantiles when the covariate is functional and when the order of the quantiles converges to one as the sample size increases. In a first time, we investigate to what extent these large conditional quantiles can still be estimated through a functional kernel estimator of the conditional survival function. Sufficient conditions on the rate of convergence of their order to one are provided to obtain asymptotically Gaussian distributed estimators. In a second time, basing on these result, a functional Weissman estimator is derived, permitting to estimate large conditional quantiles of arbitrary large order. These results are illustrated on finite sample situations.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/663e3123e719f669b565946159180b1fc8fab7ad

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Finance

In Statistics and Probability

Citations in the corpus

Nonparametric modelling for functional data: selected survey and tracks for future (2018, background): “A special attention is paid to large quantiles in [100,101].”
Non‐parametric Estimation of Extreme Risk Measures from Conditional Heavy‐tailed Distributions (2014, background): “˛njx/ is the extreme conditional quantile of level ˛n 2 .0; 1/ (for instance, Beirlant et al., 2004; Daouia et al., 2011, 2013; Gardes & Girard, 2010, 2012; Wang et al., 2012).”