Quantity quantiles linear regression

We show that the definition of the θth sample quantile as the solution to a minimization problem introduced by Koenker and Basset [1978] can be easily extended to obtain an analogous definition for the θth sample quantity quantile instead of the usual one. By means of this definition we introduce a linear regression model for quantity quantiles and analyze some properties of the residuals. In section 4 we show a brief application of the methodology proposed.