Exploring multicollinearity in quantile regression

The aim of the paper is to propose a simulation study to explore the multicollinearity problem in quantile regression, as compared to the classical linear regression. The simulation exploits the concept of a relevant subspace and relevant predictors, considering different degrees of collinearity among the involved predictors. The approach is based on principal components and consists in evaluating the degree of dependence between the predictors on the basis of the eigenvalue structure of their covariance matrix. It is well known that in case of highly intercorrelated predictors the least squares coefficients, although determinate, posses large standard errors, causing precision problems for their estimation. For this reason, results of the simulation study focus on standard errors estimated according to different collinearity levels. A possible solution based on regression on principal components is briefly presented.