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.
Citation
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
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