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18 juin 2020
- ISIDORE Id: 10670/1.1a090c...
- hal: hal-02130472
- ARXIV: 1905.06584
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info:eu-repo/semantics/altIdentifier/arxiv/1905.06584
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info:eu-repo/grantAgreement/EC/FP7/337665/EU/Parsimony and operator methods for treatment of endogeneity and multiple sources of unobserved heterogeneity/POEMH
info:eu-repo/semantics/OpenAccess
Mots-clés
Minimax Random Coefficients Adaptation Ill-posed Inverse Problem Primary 62P20 ; secondary 42A99, 62C20, 62G07, 62G08, 62G20Citer ce document
Christophe Gaillac et al., « Adaptive estimation in the linear random coefficients model when regressors have limited variation », HAL SHS (Sciences de l’Homme et de la Société), ID : 10670/1.1a090c...
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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.
