A simple recipe for making accurate parametric inference in finite sample

The algorithmic principle of the bootstrap method is quite simple: reiterate the mechanism that produces an estimator on pseudo-samples. But when it comes to estimators that are numerically complicated to obtain, the bootstrap is less attractive to use due to the numerical burden. If one estimator is hard to find, reiterating compounds this issue. Paraphrasing Emile in the French comedy La Cite de la Peur: we can implement the bootstrap when the estimator is simple to obtain or we can compute a numerically complex point estimator, but it is too computationally cumbersome to do both.