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2018 Adaptive estimation in the nonparametric random coefficients binary choice model by needlet thresholding
Eric Gautier, Erwan Le Pennec
Electron. J. Statist. 12(1): 277-320 (2018). DOI: 10.1214/17-EJS1383

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 $\mathrm{L}^{p}(\mathbb{S}^{d-1})$ 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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Eric Gautier. Erwan Le Pennec. "Adaptive estimation in the nonparametric random coefficients binary choice model by needlet thresholding." Electron. J. Statist. 12 (1) 277 - 320, 2018. https://doi.org/10.1214/17-EJS1383

Information

Received: 1 October 2016; Published: 2018
First available in Project Euclid: 12 February 2018

zbMATH: 1387.62049
MathSciNet: MR3763073
Digital Object Identifier: 10.1214/17-EJS1383

Subjects:
Primary: 62P20

JOURNAL ARTICLE
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Vol.12 • No. 1 • 2018
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