Implicitly Weighted Robust Estimation of Quantiles in Linear Regression

Abstract

Estimation of quantiles represents a very important task in econometric regression modeling and the standard regression quantiles machinery is well developed with numerous econometric applications. Although regression quantiles are commonly known as robust tools, they are vulnerable to the presence of leverage points in the data. We propose here a novel approach for the linear regression based on a specific version of the least weighted squares estimator, together with an additional estimator based only on observations between two different novel quantiles. Numerical computations reveal the new methods to perform comparably to standard regression quantiles, if the data are not contaminated by outliers. However, the new methods seem much more robust on a simulated dataset with severe leverage points. The new methods are also conceptually simple and comprehensible