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November 2020 Rate-optimal nonparametric estimation for random coefficient regression models
Hajo Holzmann, Alexander Meister
Bernoulli 26(4): 2790-2814 (November 2020). DOI: 10.3150/20-BEJ1207

Abstract

Random coefficient regression models are a popular tool for analyzing unobserved heterogeneity, and have seen renewed interest in the recent econometric literature. In this paper, we obtain the optimal pointwise convergence rate for estimating the density in the linear random coefficient model over Hölder smoothness classes, and in particular show how the tail behavior of the design density impacts this rate. In contrast to previous suggestions, the estimator that we propose and that achieves the optimal convergence rate does not require dividing by a nonparametric density estimate. The optimal choice of the tuning parameters in the estimator depends on the tail parameter of the design density and on the smoothness level of the Hölder class, and we also study adaptive estimation with respect to both parameters.

Citation

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Hajo Holzmann. Alexander Meister. "Rate-optimal nonparametric estimation for random coefficient regression models." Bernoulli 26 (4) 2790 - 2814, November 2020. https://doi.org/10.3150/20-BEJ1207

Information

Received: 1 March 2019; Revised: 1 January 2020; Published: November 2020
First available in Project Euclid: 27 August 2020

zbMATH: 07256160
MathSciNet: MR4140529
Digital Object Identifier: 10.3150/20-BEJ1207

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

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Vol.26 • No. 4 • November 2020
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