Estimation of quantile density function based on regression quantiles

We propose two estimators of quantile density function in linear regression model. The estimators, either of histogram or of kernel types, are based on regression quantiles and extend the Falk (1986) estimators based on order statistics from the location to the linear regression model. Unlike various other estimators proposed in the literature, our estimators are regression invariant and scale equivariant and hence applicable in estimation, testing, bounded-length confidence interval estimation and other inference based on L1-norm.