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Adaptive estimation in the nonparametric random coefficients binary choice model by needlet thresholding

Listed author(s):
  • Eric Gautier

    ()

    (TSE - Toulouse School of Economics - Toulouse School of Economics)

  • Erwan Le Pennec

    ()

    (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS - Centre National de la Recherche Scientifique, XPOP - Modélisation en pharmacologie de population - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en Automatique)

In the random coefficients binary choice model, a binary variable equals 1 iff an index $X^\top\beta$ is positive. The vectors $X$ and $\beta$ are independent and belong to the sphere $\mathbb{S}^{d-1}$ in $\mathbb{R}^{d}$. We prove lower bounds on the minimax risk for estimation of the density $f_{\beta}$ over Besov bodies where the loss is a power of the $L^p(\mathbb{S}^{d-1})$ norm for $1\le p\le \infty$. We show that a hard thresholding estimator based on a needlet expansion with data-driven thresholds achieves these lower bounds up to logarithmic factors.

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File URL: https://hal.inria.fr/inria-00601274v3/document
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Paper provided by HAL in its series Working Papers with number inria-00601274.

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Date of creation: 22 Sep 2016
Handle: RePEc:hal:wpaper:inria-00601274
Note: View the original document on HAL open archive server: https://hal.inria.fr/inria-00601274v3
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  1. Heckman, James & Singer, Burton, 1984. "A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data," Econometrica, Econometric Society, vol. 52(2), pages 271-320, March.
  2. Hoderlein, Stefan & Klemelä, Jussi & Mammen, Enno, 2010. "Analyzing The Random Coefficient Model Nonparametrically," Econometric Theory, Cambridge University Press, vol. 26(03), pages 804-837, June.
  3. Eric Gautier & Stefan Soderlein, 2011. "Estimating the Distribution of Treatment Effects," Working Papers 2011-25, Centre de Recherche en Economie et Statistique.
  4. Ichimura, Hidehiko & Thompson, T. Scott, 1998. "Maximum likelihood estimation of a binary choice model with random coefficients of unknown distribution," Journal of Econometrics, Elsevier, vol. 86(2), pages 269-295, June.
  5. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, 03.
  6. Chris Elbers & Geert Ridder, 1982. "True and Spurious Duration Dependence: The Identifiability of the Proportional Hazard Model," Review of Economic Studies, Oxford University Press, vol. 49(3), pages 403-409.
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