An empirical variance distribution approximation, using backtransformation from the percentile scale, for the quantile estimating function of continuous distributions

This paper demonstrates a quadratic polynomial proxy, to calculate quantile variance estimates of continuous distributions in the percentile scale, for the quantile estimating function (Koencker & Bassett). The empirical variance distribution function created by the backtransformation of the percentile scale calculations to the original measurement scale for the proxy estimator, has a step function morphology, in common with the empirical cumulative distribution function. The use of the empirical variance distribution approach to calculating the variance of the quantile regression residuals becomes a new method for calculating confidence intervals for fitted quantile regression coefficients.