@article{kuk1995,
author = {Kuk, Anthony Y. C.},
title = {Asymptotically Unbiased Estimation in Generalized Linear Models with Random Effects},
journal = {Journal of the Royal Statistical Society: Series B (Methodological)},
volume = {57},
number = {2},
pages = {395-407},
keywords = {bias correction, consistent estimator, estimating equations, monte carlo method, random effects model},
doi = {10.1111/j.2517-6161.1995.tb02035.x},
url = {https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/j.2517-6161.1995.tb02035.x},
eprint = {https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1995.tb02035.x},
abstract = {SUMMARY Obtaining estimates that are nearly unbiased has proven to be difficult when random effects are incorporated into a generalized linear model. In this paper, we propose a general method of adjusting any conveniently defined initial estimates to result in estimates which are asymptotically unbiased and consistent. The method is motivated by iterative bias correction and can be applied in principle to any parametric model. A simulation-based approach of implementing the method is described and the relationship of the method proposed with other sampling-based methods is discussed. Results from a small scale simulation study show that the method proposed can lead to estimates which are nearly unbiased even for the variance components while the standard errors are only slightly inflated. A new analysis of the famous salamander mating data is described which reveals previously undetected between-animal variation among the male salamanders and results in better prediction of mating outcomes.},
year = {1995}
}

@article{guerrier2019,
author = {Stéphane Guerrier and Elise Dupuis-Lozeron and Yanyuan Ma and Maria-Pia Victoria-Feser},
title = {Simulation-Based Bias Correction Methods for Complex Models},
journal = {Journal of the American Statistical Association},
volume = {114},
number = {525},
pages = {146-157},
year  = {2019},
publisher = {Taylor & Francis},
doi = {10.1080/01621459.2017.1380031},
url = {https://doi.org/10.1080/01621459.2017.1380031},
eprint = {https://doi.org/10.1080/01621459.2017.1380031},
abstract = { ABSTRACTAlong with the ever increasing data size and model complexity, an important challenge frequently encountered in constructing new estimators or in implementing a classical one such as the maximum likelihood estimator, is the computational aspect of the estimation procedure. To carry out estimation, approximate methods such as pseudo-likelihood functions or approximated estimating equations are increasingly used in practice as these methods are typically easier to implement numerically although they can lead to inconsistent and/or biased estimators. In this context, we extend and provide refinements on the known bias correction properties of two simulation-based methods, respectively, indirect inference and bootstrap, each with two alternatives. These results allow one to build a framework defining simulation-based estimators that can be implemented for complex models. Indeed, based on a biased or even inconsistent estimator, several simulation-based methods can be used to define new estimators that are both consistent and with reduced finite sample bias. This framework includes the classical method of the indirect inference for bias correction without requiring specification of an auxiliary model. We demonstrate the equivalence between one version of the indirect inference and the iterative bootstrap, both correct sample biases up to the order n− 3. The iterative method can be thought of as a computationally efficient algorithm to solve the optimization problem of the indirect inference. Our results provide different tools to correct the asymptotic as well as finite sample biases of estimators and give insight on which method should be applied for the problem at hand. The usefulness of the proposed approach is illustrated with the estimation of robust income distributions and generalized linear latent variable models. Supplementary materials for this article are available online. }
}

@misc{guerrier2020,
      title={A General Approach for Simulation-based Bias Correction in High Dimensional Settings},
      author={Stéphane Guerrier and Mucyo Karemera and Samuel Orso and Maria-Pia Victoria-Feser and Yuming Zhang},
      year={2020},
      eprint={2010.13687},
      archivePrefix={arXiv},
      primaryClass={math.ST},
      howpublished={\url{https://arxiv.org/pdf/2010.13687.pdf}},
      note={Version 2: 13 Nov 2020},
      URL={https://arxiv.org/pdf/2010.13687.pdf}
}
