Conditional quantile estimation by local logistic regression†

Abstract

In this article, we propose a new nonparametric estimator of the conditional quantile function. It is based on locally fitting a logistic model. We compare the new proposal with some existing methods. Those include the double-kernel technique of Yu and Jones (1998), the adjusted version of the Nadaraya–Watson estimator suggested by Hall et al. (1999) and the approach by Koenker and Bassett (1978) based on the ‘check function’ loss. The comparison is done by asymptotic mean squared error and a simulation study. The four estimators have the same asymptotic variance, but their first-order biases are different. We also propose a new automatic smoothing parameter selection method in quantile estimation. We analyze the finite sample properties of the quantile estimators using the proposed bandwidth selectors. We find that the new method outperforms the others in most cases of the numerical experiments.