Topic

Excess-Risk Consistency of Group-Hard Thresholding Estimator in Robust Estimation of Gaussian Mean

Arshak  Minasyan

 

Department of Mathematics – Yerevan State University,
YerevaNN Research Lab

 

Abstract:

 

In this work we introduce the notion of the excess risk in the setup
of estimation of the Gaussian mean when the observations are corrupted by outliers.
It is known that the sample mean loses its good properties in the presence of
outliers \cite{huber1,huber2}. In addition, even the sample median is
not minimax-rate-optimal in the multivariate setting. The optimal rate of the minimax
risk in this setting was established by \cite{chao_gao}. However, even these
minimax-rate-optimality results do not quantify how fast the risk in the
contaminated model approaches the risk in the uncontaminated model when
the rate of contamination goes to zero. The present paper does a first step
in filling this gap by showing that the group hard thresholding estimator has
an excess risk that goes to zero when the corruption rate approaches zero.

Discussion Room: Excess-Risk Consistency of Group-Hard Thresholding Estimator in Robust Estimation of Gaussian Mean

 

minasyan@yerevann.com

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