Title: Prediction intervals in quantile regression
Authors: Ida Bauer - University of Passau (Germany) [presenting]
Harry Haupt - University of Passau (Germany)
Markus Fritsch - University of Passau (Germany)
Abstract: A simulation approach is exploited to investigate prediction intervals in different settings for (generalized) least squares and quantile regression. It provides an extensive and structured overview of different approaches to quantile-based prediction intervals described in the literature and tries a fair comparison to suitable (case-specific) alternatives. We start with a case that complies with all requirements for accurate LS prediction intervals and subsequently relax distributional assumptions. This should allow contrasting strengths and potential drawbacks of each and every method. Evaluation of the accuracy of the intervals is performed by comparing empirical coverage levels as well as taking a look at interval width and percentage of overlap. Further issues to be discussed are whether the fact that regression quantiles used for interval construction are point estimates and thus subject to variation themselves has been recognized in the literature so far and ---if so--- whether the latter provides a remedy. We also touch upon the topic of quantile crossing, which is a particular issue especially in the context of prediction intervals.