Section:
New Results
Conditional quantile estimation through optimal quantization: theoretical aspects
The following result has been obtained by J. Saracco (Inria CQFD) and I. Charlier (Inria CQFD), D. Paindaveine (ULB).
In this work, we use quantization to construct a nonparametric estimator of conditional
quantiles of a scalar response given a d-dimensional vector of covariates . First we
focus on the population level and show how optimal quantization of , which consists in
discretizing by projecting it on an appropriate grid of points, allows to approximate
conditional quantiles of given .
We show that this approximation is arbitrarily good as
goes to infinity and provide a rate of convergence for the approximation error. Then we turn
to the sample case and define an estimator of conditional quantiles based on quantization
ideas. We prove that this estimator is consistent for its fixed- population counterpart.
The results are illustrated on a numerical example.