Abstract:
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Constructing estimators that are robust to data contamination is non-trivial in high dimensional settings, where the number of variables p diverges with the sample size n. Indeed, to be consistent, these estimators typically rely on a non-negligible correction term with no closed-form expression. Numerical approximation to this term can introduce finite sample bias that is magnified under high dimensional regimes. To address these challenges, we propose a simulation-based bias correction technique, which allows us to easily construct robust estimators with reduced finite sample bias for complex models in high dimensional settings. Our estimators also enjoy statistical properties of consistency and asymptotic normality, while remaining computationally efficient using the Iterative Bootstrap method of Kuk (1995). These results are highlighted with different simulation studies, including logistic regression models with and without random effect and parametric Cox proportional hazards model, from which we also observe that our estimators are actually comparable, in terms of finite sample mean squared error, to classical maximum likelihood estimators under no data contamination.
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