Conditional quantiles: An operator-theoretical approach

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...

Predicting Conditional Quantiles via Reduction to Classification

We show how to reduce the process of predicting conditional quantiles (and the median in particular) to solving classification. The accompanying theoretical statement shows that the regret of the classifier bounds the regret of the quantile regression under a quantile loss. We also test this reduction empirically against existing quantile regression methods on large real-world datasets and disc...

Nonparametric Prewhitening Estimators for Conditional Quantiles

We define a nonparametric prewhitening method for estimating conditional quantiles based on local linear quantile regression. We characterize the bias, variance and asymptotic normality of the proposed estimator. Under weak conditions our estimator can achieve bias reduction and have the same variance as the local linear quantile estimators. A small set of Monte Carlo simulations is carried out...

Functional kernel estimators of large conditional quantiles