On estimation of nonsmooth functionals of sparse normal means

2018/05/28 by Olivier Collier, Collier, Olivier, Laëtitia Comminges +3
Decision Sciences · Mathematics · #FOS: Mathematics #Probability and Risk Models #Risk and Portfolio Optimization #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1805.10791

openalex publication_date 2018/05/28 · arxiv created 2019/10/05 · arxiv updated 2019/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the problem of estimation of the value N_gamma(θ) = sum(i=1)^d |θ_i|^gamma for 0 < gamma <= 1 based on the observations y_i = θ_i + εξ_i, i = 1,...,d, where θ= (θ₁,...,θ_d) are unknown parameters, ε>0 is known, and ξ_i are i.i.d. standard normal random variables. We prove that the non-asymptotic minimax risk on the class B₀(s) of s-sparse vectors and we propose estimators achieving the minimax rate.

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