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Burgard JP, Krause J, Kreber D, Morales D. The generalized equivalence of regularization and min–max robustification in linear mixed models. Stat Pap (Berl) 2021. [DOI: 10.1007/s00362-020-01214-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Abstract
AbstractThe 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.
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Zhang Q. High-Dimensional Mediation Analysis with Applications to Causal Gene Identification. STATISTICS IN BIOSCIENCES 2021. [DOI: 10.1007/s12561-021-09328-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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Estimation of regional transition probabilities for spatial dynamic microsimulations from survey data lacking in regional detail. Comput Stat Data Anal 2021. [DOI: 10.1016/j.csda.2020.107048] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Burgard JP, Krause J, Münnich R. An elastic net penalized small area model combining unit- and area-level data for regional hypertension prevalence estimation. J Appl Stat 2020; 48:1659-1674. [DOI: 10.1080/02664763.2020.1765323] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- J. P. Burgard
- Department of Economic and Social Statistics, Trier University, Trier, Germany
| | - J. Krause
- Department of Economic and Social Statistics, Trier University, Trier, Germany
| | - R. Münnich
- Department of Economic and Social Statistics, Trier University, Trier, Germany
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