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

Eric Gautier and Erwan Le Pennec (erwan.le-pennec@polytechnique.edu)
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Erwan Le Pennec: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, XPOP - Modélisation en pharmacologie de population - CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique - Centre Inria de l'Institut Polytechnique de Paris - Centre Inria de Saclay - Inria - Institut National de Recherche en Informatique et en Automatique

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Abstract: 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.

Keywords: Discrete choice models; minimax rate optimality; needlets; random coefficients; data-driven thresholding; adaptation; inverse problems (search for similar items in EconPapers)
Date: 2017-11-28
New Economics Papers: this item is included in nep-dcm and nep-ecm
Note: View the original document on HAL open archive server: https://inria.hal.science/inria-00601274v4
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Related works:
Working Paper: Adaptive Estimation in the Nonparametric Random Coefficients Binary Choice Model by Needlet Thresholding (2011)
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