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• W2990736268 abstract "We review some basic ideas of the robust statistics literature and define tools that allows us to construct robust statistical procedures. We show how these ideas, originally developed for fixed dimensional settings, can also be applied to high-dimensional problems where the number of unknown parameters can be larger than the sample size. In particular, we build on the theory of M-estimators and adapt it to handle the problems of high-dimensional regression and covariance matrix estimation via regularization. For the former problem we show that penalized M-estimators for high-dimensional generalized linear models can lead to estimators that are consistent when the data is nice and contains no contaminated observations, while importantly remaining stable in the presence of a small fraction of outliers. For the problem of covariance estimation we show that M-estimators be used to significantly weaken the typical requirement of having sub-Gaussian distributions to assuming only a few finite moments. This relaxation cannot be achieved by regularizing the sample covariance as in classical fixed dimensional regimes." @default.
• W2990736268 created "2019-12-05" @default.
• W2990736268 creator A5017137031 @default.
• W2990736268 date "2019-11-29" @default.
• W2990736268 modified "2023-09-28" @default.
• W2990736268 title "Robust Methods for High-Dimensional Regression and Covariance Matrix Estimation" @default.
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• W2990736268 doi "https://doi.org/10.1007/978-3-030-31150-6_19" @default.
• W2990736268 hasPublicationYear "2019" @default.
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