Optimal adaptive estimation of linear functionals under sparsity
Statistics Theory
2017-10-09 v2 Statistics Theory
Abstract
We consider the problem of estimation of a linear functional in the Gaussian sequence model where the unknown vector theta in R^d belongs to a class of s-sparse vectors with unknown s. We suggest an adaptive estimator achieving a non-asymptotic rate of convergence that differs from the minimax rate at most by a logarithmic factor. We also show that this optimal adaptive rate cannot be improved when s is unknown. Furthermore, we address the issue of simultaneous adaptation to s and to the variance sigma^2 of the noise. We suggest an estimator that achieves the optimal adaptive rate when both s and sigma^2 are unknown.
Cite
@article{arxiv.1611.09744,
title = {Optimal adaptive estimation of linear functionals under sparsity},
author = {Olivier Collier and Laëtitia Comminges and Alexandre B. Tsybakov and Nicolas Verzélen},
journal= {arXiv preprint arXiv:1611.09744},
year = {2017}
}