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arXiv · 1805.10791

On estimation of nonsmooth functionals of sparse normal means

Olivier Collier·Laëtitia Comminges·Alexandre B. Tsybakov
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Abstract

We study the problem of estimation of the value N_gamma(\theta) = sum(i=1)^d |\theta_i|^gamma for 0 < gamma <= 1 based on the observations y_i = \theta_i + \epsilon\xi_i, i = 1,...,d, where \theta = (\theta_1,...,\theta_d) are unknown parameters, \epsilon>0 is known, and \xi_i are i.i.d. standard normal random variables. We prove that the non-asymptotic minimax risk on the class B_0(s) of s-sparse vectors and we propose estimators achieving the minimax rate.

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Olivier Collier, Laëtitia Comminges, Alexandre B. Tsybakov. 2018-05-28. On estimation of nonsmooth functionals of sparse normal means. https://arxiv.org/abs/1805.10791

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