Before revision:  As a by-product, we also construct CIs for tail features of the coefficients in the random coefficient regression model. The new CIs are robustly valid without parametric assumptions and exhibit superior small sample coverage and length properties than alternative nonparametric approaches based on asymptotic normality.
After revision:  As a by-product, we also construct CIs for extremal quantiles of coefficients in linear random coefficient models. For any fixed k, the CIs are uniformly valid without parametric assumptions and exhibit superior small sample coverage and length properties than alternative nonparametric approaches based on asymptotic normality.