Random coefficient regression models are important in representing linear models with heteroscedastic errors and in unifying the study of classical fixed effects and random effects linear models. For prediction intervals and for bootstrapping in random coefficient regressions, it is necessary to estimate the distributions of the random coefficients consistently. We show that this is often possible and provide practical representative estimators of these distributions.
"Estimating Coefficient Distributions in Random Coefficient Regressions." Ann. Statist. 20 (4) 1970 - 1984, December, 1992. https://doi.org/10.1214/aos/1176348898