Abstract : We construct a nonparametric estimator of conditional quantiles of Y given X = x using optimal quantization. Conditional quantiles are particularly of interest when the condi-tional mean is not representative of the impact of the covariable X on the dependent variable Y . L p -norm optimal quantization is a discretizing method used since the 1950's in engineer-ing. It allows to construct the best approximation of a continuous law with a discrete law with support of size N . The aim of this work is then to use optimal quantization to construct con-ditional quantile estimators. We study the convergence of the approximation (N → ∞) and the consistency of the resulting estimator for this fixed-N approximation. This estimator was implemented in R in order to evaluate the numerical behavior and to compare it with existing methods.
https://hal.inria.fr/hal-01109009
Contributor : Isabelle Charlier
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Submitted on : Tuesday, January 27, 2015 - 3:00:31 PM
Last modification on : Thursday, January 11, 2018 - 6:22:11 AM
Long-term archiving on : Friday, September 11, 2015 - 9:02:18 AM
