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

Christophe Gaillac (1, 2) , Eric Gautier (1, 3)

1 TSE-R - Toulouse School of Economics
2 CREST - Centre de Recherche en Économie et Statistique
3 UT Capitole - Université Toulouse Capitole

We consider a linear model where the coefficients - intercept and slopes - are random with a distribution in a nonparametric class and independent from the regressors. The main drawback of this model is that identification usually requires the regressors to have a support which is the whole space. This is rarely satisfied in practice. Rather, in this paper, the regressors can have a support which is a proper subset. This is possible by assuming that the slopes do not have heavy tails. Lower bounds on the supremum risk for the estimation of the joint density of the random coefficients 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. The corresponding R package is RandomCoefficients on CRAN.R.

Mots clés: Ill-posed Inverse Problem; Adaptation; Random Coefficients; Minimax; Analytic continuation

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Economies et finances; Méthodes et statistiques

Christophe Gaillac, Eric Gautier. Adaptive estimation in the linear random coefficients model when regressors have limited variation. 2019. ⟨hal-02130472v3⟩