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

Abstract

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 slopes do not have heavy tails, the joint density of the random coecients is identied. 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.

Replaces

Christophe Gaillac, and Eric Gautier, “Adaptive estimation in the linear random coefficients model when regressors have limited variation”, TSE Working Paper, n. 19-1026, July 2019.

Reference

Christophe Gaillac, and Eric Gautier, “Adaptive estimation in the linear random coefficients model when regressors have limited variation”, Bernoulli, vol. 28, n. 1, February 2022, pp. 504–524.