Quantile Regression Estimation Using Non-Crossing Constraints

Abstract

In this article we are concerned with a collection of multiple linear regressions that enable the researcher to gain an impression of the entire conditional distribution of a response variable given a set of explanatory variables. More specifically, we investigate the advantage of using a new method to estimate a bunch of non-crossing quantile regressions hyperplanes. The main tool is a weighting system of the data elements that aims to reduce the effect of contamination of the sampled population on the estimated parameters by diminishing the effect of outliers. The performances of the new estimators are evaluated on a number of data sets. We had considerable success with avoiding intersections and in the same time improving the global fitting of conditional quantile regressions. We conjecture that in other situations (e.g., data with high level of skewness, non-constant variances, unusual and imputed data) the method of weighted non-crossing quantiles will lead to estimators with good robustness properties.