  This paper deals with improvement of linear quantile regression, when there
are a few distinct values of the covariates but many replicates. On can improve
asymptotic efficiency of the estimated regression coefficients by using
suitable weights in quantile regression, or simply by using weighted least
squares regression on the conditional sample quantiles. The asymptotic
variances of the unweighted and weighted estimators coincide only in some
restrictive special cases, e.g., when the density of the conditional response
has identical values at the quantile of interest over the support of the
covariate. The dominance of the weighted estimators is demonstrated in a
simulation study, and through the analysis of a data set on tropical cyclones.
