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This paper deals with improvement of linear quantile regression, when thereare a few distinct values of the covariates but many replicates. On can improveasymptotic efficiency of the estimated regression coefficients by usingsuitable weights in quantile regression, or simply by using weighted leastsquares regression on the conditional sample quantiles. The asymptoticvariances of the unweighted and weighted estimators coincide only in somerestrictive special cases, e.g., when the density of the conditional responsehas identical values at the quantile of interest over the support of thecovariate. The dominance of the weighted estimators is demonstrated in asimulation study, and through the analysis of a data set on tropical cyclones.

Improving linear quantile regression for replicated data