Quantiles for counts

Abstract

This paper studies the estimation of conditional quantiles of counts. Given the discreteness of the data, some smoothness has to be artificially imposed on the problem. The methods currently available to estimate quantiles of count data either assume that the counts result from the discretization of a continuous process, or are based on a smoothed objective function. However, these methods have several drawbacks. We show that it is possible to smooth the data in a way that allows inference to be performed using standard quantile regression techniques. The performance and implementation of the estimator are illustrated by simulations and an application.