A location-scale model for non-crossing expectile curves

In quantile smoothing, crossing of the estimated curves is a common nuisance, in particular with small data sets and dense sets of quantiles. Similar problems arise in expectile smoothing. We propose a novel method to avoid crossings. It is based on a location-scale model for expectiles and estimates all expectile curves simultaneously in a bundle using iterative least asymmetrically weighted squares. In addition, we show how to estimate a density non-parametrically from a set of expectiles. The model is applied to two data sets.