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Title: Accurate parametric inference in high dimensional settings: A step beyond the bootstrap Authors:  Maria-Pia Victoria-Feser - University of Geneva (Switzerland) [presenting]
Stephane Guerrier - University of Geneva (Switzerland)
Mucyo Karemera - University of Geneva (Switzerland)
Samuel Orso - University of Geneva (Switzerland)
Abstract: Accurate estimation and inference in finite sample is important especially when the available data are complex, like when they include mixed types of measurements, they are dependent in several ways, there are missing data, outliers, etc. Indeed, the more complex the data (hence the models), the less accurate are asymptotic theory results in finite samples. This is in particular the case, for example, with logistic regression, with possibly also random effects to account for the dependence structure between the outcomes, or more generally, when the likelihood function or the estimating equations have non closed-form expression. Moreover, resampling techniques such as the Bootstrap can also be quite inaccurate in these settings, unless (complex) corrections are provided. We propose instead a simulation based method, the Iterative Bootstrap (IB), that can be used, very generally, to obtain a) unbiased estimators in high dimensional settings, b) finite sample distributions for inference, with, under suitable conditions, the exact probability coverage property. The method is based on an initial estimator, that does not need to be consistent and can hence be chosen for numerical convenience, and/or can have some desirable properties such as robustness. We present the main theoretical results and the relationships with well-established methods, as well as simulation studies involving complex models and different estimators.