A smooth conditional quantile estimator and related applications of conditional empirical processes

A Smooth Nonparametric Conditional Quantile Frontier Estimator

Traditional estimators for nonparametric frontier models (DEA, FDH) are very sensitive to extreme values/outliers. Recently, Aragon, Daouia, and Thomas-Agnan (2005) proposed a nonparametric α-frontier model and estimator based on a suitably defined conditional quantile which is more robust to extreme values/outliers. Their estimator is based on a nonsmooth empirical conditional distribution. In...

Asymptotics of Conditional Empirical Processes

We investigate asymptotic approximations of two estimators of the conditional empirical process of Y given X= x, leading to a functional law of the iterated logarithm. Our main results show that the weak behavior of the conditional empirical processes at a given x is essentially the same as that of the empirical process, although the rates now depend on the bandwidth. We examine the kernel esti...

CQN (Conditional Quantile Normalization)

Conditional Quantile Processes Based on Series or Many Regressors

Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric QR series framework, covering many regressors as a special case, for performing inference on the entire conditional quantile function and its linear functionals. ...

Conditional Expectation as Quantile Derivative

For a linear combination ∑ uj Xj of random variables, we are interested in the partial derivatives of its α-quantile Qα(u) regarded as a function of the weight vector u = (uj). It turns out that under suitable conditions on the joint distribution of (Xj) the derivatives exist and coincide with the conditional expectations of the Xi given that ∑ uj Xj takes the value Qα(u). Moreover, using this ...