I have a dependent achievement score variable which is continuous, but is also of uneven density, with small areas of high density followed by areas of low density. If I do a quantile regression with a single binary RHS variable, I find that there might be a significant gap (ie coefficient) at the 10th percentile (say), followed by no gap at the 15th, then a significant gap at the 20th and so on. These variations come from the uneven density. The heaping of the density is (probably) not particularly meaningful, but merely represents the limitations in the way the dependent variable is constructed. Is there a way to smooth the quantile regression results? For example, to fit a cubic function of percentile across the various quantiles?
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