Along 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, as shown in Guerrier, et al. (2018), based on a biased or even inconsistent estimator, several simulation based methods can be used to define new estimators that are both consistent and numerically very fast to compute in complex settings. This framework includes the classical method of indirect inference without requiring specification of an auxiliary model. We illustrate the use of simulation based estimation, using intitial estimators that are fast to compute, in the framework of Generalized Linear Models and (exploratory) factor analysis with binary outcomes when $p>n$, with large $p$.