Minimax optimal estimators for general additive functional estimation
Statistics Theory
2019-08-30 v1 Statistics Theory
Abstract
In this paper, we observe a sparse mean vector through Gaussian noise and we aim at estimating some additive functional of the mean in the minimax sense. More precisely, we generalize the results of (Collier et al., 2017, 2019) to a very large class of functionals. The optimal minimax rate is shown to depend on the polynomial approximation rate of the marginal functional, and optimal estimators achieving this rate are built.
Cite
@article{arxiv.1908.11070,
title = {Minimax optimal estimators for general additive functional estimation},
author = {Olivier Collier and Laëtitia Comminges},
journal= {arXiv preprint arXiv:1908.11070},
year = {2019}
}