Many univariate robust estimators are based on quantiles. As already theoretically pointed out by Fernholz (in J. Stat. Plan. Inference 57(1), 29–38, <CitationRef CitationID="CR7">1997</CitationRef>), smoothing the empirical distribution function with an appropriate kernel and bandwidth can reduce the variance and mean squared error...</citationref>

<Para ID="Par1">In this paper, we present a method for estimating the conditional distribution function of the model error. Given the covariates, the conditional mean function is modeled as a partial linear model, and the conditional distribution function of model error is modeled as a single-index model. To...</para>