Affiliation:
1. LJK, Université Grenoble Alpes, Avenue Centrale, Domaine Universitaire de Saint-Martin-d’Hères, France
2. Georgia Institute of Technology, Atlanta, GA, USA
Abstract
Abstract
In this paper we build provably near-optimal, in the minimax sense, estimates of linear forms and, more generally, ‘$N$-convex functionals’ (an example being the maximum of several fractional-linear functions) of unknown ‘signal’ from indirect noisy observations, the signal assumed to belong to the union of finitely many given convex compact sets. Our main assumption is that the observation scheme in question is good in the sense of Goldenshluger et al. (2015, Electron. J. Stat., 9, 1645–1712), the simplest example being the Gaussian scheme, where the observation is the sum of linear image of the signal and the standard Gaussian noise. The proposed estimates, same as upper bounds on their worst-case risks, stem from solutions to explicit convex optimization problems, making the estimates ‘computation-friendly’.
Funder
LabEx PERSYVAL-Lab
Programme Gaspard Monge
National Science Foundation
Publisher
Oxford University Press (OUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Numerical Analysis,Statistics and Probability,Analysis
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献