  Performing inference such a computing confidence intervals is traditionally
done, in the parametric case, by first fitting a model and then using the
estimates to compute quantities derived at the asymptotic level or by means of
simulations such as the ones from the family of bootstrap methods. These
methods require the derivation and computation of a consistent estimator that
can be very challenging to obtain when the models are complex as is the case
for example when the data exhibit some types of features such as censoring,
missclassification errors or contain outliers. In this paper, we propose a
simulation based inferential method, the implicit bootstrap, that bypasses the
need to compute a consistent estimator and can therefore be easily implemented.
While being transformation respecting, we show that under similar conditions as
for the studentized bootstrap, without the need of a consistent estimator, the
implicit bootstrap is first and second order accurate. Using simulation
studies, we also show the coverage accuracy of the method with data settings
for which traditional methods are computationally very involving and also lead
to poor coverage, especially when the sample size is relatively small. Based on
these empirical results, we also explore theoretically the case of exact
inference.
