Robust multivariate mean estimation: The optimality of trimmed mean
Gábor Lugosi, Shahar Mendelson
Abstract
We consider the problem of estimating the mean of a random vector based on i.i.d. observations and adversarial contamination. We introduce a multivariate extension of the trimmed-mean estimator and show its optimal performance under minimal conditions.
Topics & Concepts
Truncated meanEstimatorMultivariate statisticsMathematicsTrimmed estimatorExtension (predicate logic)Multivariate random variableStatisticsEstimationComputer scienceRandom variableMinimax estimatorMinimum-variance unbiased estimatorEngineeringProgramming languageSystems engineeringAdvanced Statistical Methods and ModelsStatistical Methods and InferenceSurvey Sampling and Estimation Techniques