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arXiv · 1908.11070

Minimax optimal estimators for general additive functional estimation

Olivier Collier·Laëtitia Comminges
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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.

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Olivier Collier, Laëtitia Comminges. 2019-08-29. Minimax optimal estimators for general additive functional estimation. https://arxiv.org/abs/1908.11070

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