Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/286749 
Year of Publication: 
2021
Citation: 
[Journal:] Statistical Papers [ISSN:] 1613-9798 [Volume:] 62 [Issue:] 6 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2021 [Pages:] 2857-2883
Publisher: 
Springer, Berlin, Heidelberg
Abstract: 
The connection between regularization and min–max robustification in the presence of unobservable covariate measurement errors in linear mixed models is addressed. We prove that regularized model parameter estimation is equivalent to robust loss minimization under a min–max approach. On the example of the LASSO, Ridge regression, and the Elastic Net, we derive uncertainty sets that characterize the feasible noise that can be added to a given estimation problem. These sets allow us to determine measurement error bounds without distribution assumptions. A conservative Jackknife estimator of the mean squared error in this setting is proposed. We further derive conditions under which min-max robust estimation of model parameters is consistent. The theoretical findings are supported by a Monte Carlo simulation study under multiple measurement error scenarios.
Subjects: 
Measurement errors
Regularized regression
Robust best prediction
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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