The robust desparsified lasso and the focused information criterion for high-dimensional generalized linear models

The classical lasso estimation for sparse, high-dimensional regression models is typically biased and lacks the oracle properties. The desparsified versions of the lasso have been proposed in the literature that attempt to overcome these drawbacks. In this paper, we propose the outliers-robust versi...

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Bibliographic Details
Published in:Statistics (Berlin, DDR) DDR), 2023-01, Vol.57 (1), p.1-25
Main Authors: Pandhare, S. C., Ramanathan, T. V.
Format: Article
Language:English
Subjects:
Criteria
Desparsified lasso
focused information criterion
generalized linear models
high-dimensional asymptotics
nodewise regression
Outliers (statistics)
Regression models
robust estimation
Robustness (mathematics)
Statistical models
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Summary:The classical lasso estimation for sparse, high-dimensional regression models is typically biased and lacks the oracle properties. The desparsified versions of the lasso have been proposed in the literature that attempt to overcome these drawbacks. In this paper, we propose the outliers-robust version of the desparsified lasso for high dimensional generalized linear models. The robustness, consistency and high dimensional asymptotics are investigated rigorously in a general framework of M-estimation under potential model misspecification. The desparsification mechanism is subsequently utilized to construct the focused information criterion (FIC) thereby facilitating robust, focused model selection in high dimensions. The applications are demonstrated with the Poisson regression under robust quasilikelihood loss function. The empirical performance of the proposed methods is examined via simulations and a real data example.
ISSN:0233-1888
1029-4910
DOI:10.1080/02331888.2022.2154769