Proposes a scale-calibrated median-of-means estimator for robust aggregation of distributed PCA estimates on the product of Euclidean space and Grassmann manifold.
arXiv preprint arXiv:1112.3914 , year=
6 Pith papers cite this work. Polarity classification is still indexing.
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Defines threshold breakdown point and m-sensitivity for M-estimators, derives their properties, extends to hypothesis testing, and supplies consistency, asymptotic normality, and multiplier bootstrap results.
Realisable epsilon-contamination models for MNAR data yield minimax mean estimation rates that decompose into MCAR plus robust terms and remain consistent for Gaussian bases even as missingness and epsilon both tend to 1.
New smoothed random-perturbation estimators for the mean achieve exponential concentration bounds using only finite second-moment assumptions.
Derives VC-dimension-based error bounds for MOM mean estimators and introduces MOM halfspace depth estimator under finite second moment assumptions.
Develops truncated-gradient mirror descent algorithms for robust convex stochastic optimization and establishes sub-Gaussian confidence bounds under weak noise tail assumptions in convex and strongly convex cases.
citing papers explorer
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Scale-Calibrated Median-of-Means for Robust Distributed Principal Component Analysis
Proposes a scale-calibrated median-of-means estimator for robust aggregation of distributed PCA estimates on the product of Euclidean space and Grassmann manifold.
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The Threshold Breakdown Point
Defines threshold breakdown point and m-sensitivity for M-estimators, derives their properties, extends to hypothesis testing, and supplies consistency, asymptotic normality, and multiplier bootstrap results.
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Estimation beyond Missing (Completely) at Random
Realisable epsilon-contamination models for MNAR data yield minimax mean estimation rates that decompose into MCAR plus robust terms and remain consistent for Gaussian bases even as missingness and epsilon both tend to 1.
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Distribution-robust mean estimation via smoothed random perturbations
New smoothed random-perturbation estimators for the mean achieve exponential concentration bounds using only finite second-moment assumptions.
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Error bounds of Median-of-means estimators with VC-dimension
Derives VC-dimension-based error bounds for MOM mean estimators and introduces MOM halfspace depth estimator under finite second moment assumptions.
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Algorithms of Robust Stochastic Optimization Based on Mirror Descent Method
Develops truncated-gradient mirror descent algorithms for robust convex stochastic optimization and establishes sub-Gaussian confidence bounds under weak noise tail assumptions in convex and strongly convex cases.