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

2011/06/17 by Gautier, Eric, Pennec, Erwan Le · 1 citation
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1106.3503

Abstract

In the random coefficients binary choice model, a binary variable equals 1 iff an index X^\topβ is positive.The vectors X and β are independent and belong to the sphere \mathbbS^d-1 in ℝ^d.We prove lower bounds on the minimax risk for estimation of the density f_β over Besov bodies where the loss is a power of the L^p(\mathbbS^d-1) norm for 1≤ p≤ ∞. 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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