Minimax optimal estimators for general additive functional estimation

2019/08/29 by Olivier Collier, Collier, Olivier, Laëtitia Comminges +1
Mathematics · Medicine · #FOS: Mathematics #Liver Disease Diagnosis and Treatment #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1908.11070

openalex publication_date 2019/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Minimax Optimal Estimators for Additive Scalar Functionals of Discrete Distributions
• Minimax rate of testing in sparse linear regression
• Minimax estimation of linear and quadratic functionals on sparsity\n classes

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