Quantile estimation for neural networks

Abstract

Quantile estimation in nonlinear regression is a very important task with interesting applications. The established methodology for linear regression, known as regression quantiles, has been also extended to nonlinear regression in a straightforward way, however only under the assumption of a known regression function (up to parameters). Our main contribution is devoted to quantile estimator for nonlinear regression, without specifying the regression function. Particularly, we propose new estimates of quantiles based on multilayer perceptrons or radial basis function neural networks. The performance of the novel methods for linear as well as nonlinear context is illustrated on real and simulated datasets, while their robustness is clearly revealed.