On estimating conditional quantiles and distribution functions

This paper looks at ways of estimating the conditional distribution of a random variable Y given a vector X of covariates. We focus on cases where the investigator would like to avoid strong parametric assumptions but the set of covariates is large enough, relative to the available data, to make it problematic to apply standard nonparametric methods because of the well known "curse of dimensionality" problem. In these cases, estimating the conditional quantile function has become increasingly popular. An alternative is to estimate instead the conditional distribution function. Although the choice between these two equivalent representations depends to a large extent on which is more easily interpretable given the purposes of the analysis, considerations of statistical convenience should also be taken into account. We argue that such considerations tend to favor estimating the conditional distribution function directly.