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

Christophe Gaillac and Eric Gautier

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Abstract: We consider a linear model where the coefficients - intercept and slopes - are random with a law in a nonparametric class and independent from the regressors. Identification often requires the regressors to have a support which is the whole space. This is hardly ever the case in practice. Alternatively, the coefficients can have a compact support but this is not compatible with unbounded error terms as usual in regression models. In this paper, the regressors can have a support which is a proper subset but the slopes (not the intercept) do not have heavy-tails. Lower bounds on the supremum risk for the estimation of the joint density of the random coefficients density are obtained for a wide range of smoothness, where some allow for polynomial and nearly parametric rates of convergence. We present a minimax optimal estimator, a data-driven rule for adaptive estimation, and made available a R package.

Keywords: Minimax; Random Coefficients; Adaptation; Ill-posed Inverse Problem (search for similar items in EconPapers)
Date: 2020-06-18
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (2)

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Related works:
Working Paper: Adaptive estimation in the linear random coefficients model when regressors have limited variation (2021)
Working Paper: Adaptive estimation in the linear random coefficients model when regressors have limited variation (2019)
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