  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 and statistical properties is often
accepted. However, numerically efficient estimators that are altogether
unbiased, consistent and asymptotically normal in high dimensional problems
would generally be ideal. In this paper, we set a general framework from which
such estimators can easily be derived for wide classes of models. This
framework is based on the concepts that underlie simulation-based estimation
methods such as indirect inference. 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. We consider an algorithm, namely the Iterative Bootstrap
(IB), to efficiently compute simulation-based estimators by showing its
convergence properties. Within this framework we also prove the properties of
simulation-based estimators, more specifically the unbiasedness, consistency
and asymptotic normality when the number of parameters is allowed to increase
with the sample size. Therefore, an important implication of the proposed
approach is that it allows to obtain unbiased estimators in finite samples.
Finally, we study this approach when applied to three common models, namely
logistic regression, negative binomial regression and lasso regression.
