On estimation of nonsmooth functionals of sparse normal means
Statistics Theory
2019-10-08 v2 Statistics Theory
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.
Keywords
Cite
@article{arxiv.1805.10791,
title = {On estimation of nonsmooth functionals of sparse normal means},
author = {Olivier Collier and Laëtitia Comminges and Alexandre B. Tsybakov},
journal= {arXiv preprint arXiv:1805.10791},
year = {2019}
}