Adaptive estimation in the linear random coefficients model when regressors have limited variation

We consider a linear model where the coefficients-intercept and slopes-are random and independent from regressors which support is a proper subset. When the density has finite weighted L 2 norm, for well chosen weights, the joint density of the random coefficients is identified. Lower bounds on the supremum risk for the estimation of the density are derived for this model and a related white noise model. We present an estimator, its rates of convergence, and a data-driven rule which delivers adaptive estimators. An R package RandomCoefficients that implements our estimator is available on CRAN.R.