A weighted quantile regression for randomly truncated data

Quantile regression offers great flexibility in assessing covariate effects on the response. In this article, based on the weights proposed by He and Yang (2003), we develop a new quantile regression approach for left truncated data. Our method leads to a simple algorithm that can be conveniently implemented with R software. It is shown that the proposed estimator is strongly consistent and asymptotically normal under appropriate conditions. We evaluate the finite sample performance of the proposed estimators through extensive simulation studies.