Title: Improving linear quantile regression for replicated data
Authors: Kausihik Jana - Imperial College London (United Kingdom) [presenting]
Debasis Sengupta - Indian Statistical Institute (India)
Abstract: An improvement of linear quantile regression is provided when there are a few distinct values of the covariates but many replicates. On can improve the 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.