Title: On the properties of simulation-based estimators in high dimensions
Authors: Stephane Guerrier - Penn State (United States)
Maria-Pia Victoria-Feser - University of Geneva (Switzerland)
Yanyuan Ma - The Pennsylvania State University (United States)
Samuel Orso - University of Geneva (Switzerland)
Mucyo Karemera - University of Geneva (Switzerland) [presenting]
Abstract: Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase with the sample size bringing standard inferential procedures to incur significant loss in terms of performance. Moreover, the complexity of statistical models is also increasing thereby entailing important computational challenges in constructing new estimators or in implementing classical ones. A trade-off between numerical complexity (e.g. approximations of the likelihood function) and statistical properties is often accepted. However, numerically efficient estimators that are altogether unbiased, consistent and asymptotically normal in high-dimensional problems would be advantageous, especially for real data applications. We set a general framework from which such estimators can be easily derived for wide classes of models. The approach allows various extensions compared to previous results as it is adapted to possibly inconsistent estimators and is applicable to discrete models and/or models with a large number of parameters (compared to the sample size). We consider an algorithm, namely the Iterative Bootstrap, to efficiently compute simulation-based estimators by showing its convergence property.