Variable selection in heteroscedastic single-index quantile regression

We propose a new algorithm for simultaneous variable selection and parameter estimation for the single-index quantile regression (SIQR) model. The proposed algorithm, which is non iterative, consists of two steps. Step 1 performs an initial variable selection method. Step 2 uses the results of Step 1 to obtain better estimation of the conditional quantiles and, using them, to perform simultaneous variable selection and estimation of the parametric component of the SIQR model. It is shown that the initial variable selection method consistently estimates the relevant variables, and the estimated parametric component derived in Step 2 satisfies the oracle property.