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

3 XPOP - Modélisation en pharmacologie de population
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
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.
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Cited literature [27 references]

https://hal.inria.fr/inria-00601274
Contributor : Erwan Le Pennec Connect in order to contact the contributor
Submitted on : Tuesday, November 28, 2017 - 11:56:02 AM
Last modification on : Wednesday, June 9, 2021 - 10:00:17 AM

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### Identifiers

• HAL Id : inria-00601274, version 4
• ARXIV : 1106.3503

### Citation

Eric Gautier, Erwan Le Pennec. Adaptive estimation in the nonparametric random coefficients binary choice model by needlet thresholding. 2017. ⟨inria-00601274v4⟩

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