the computation of cumbersome expectations nor the, potentially expensive, calculation of $M$-estimates from simulated samples. Specifically, and as noted in the last row of Table \[br\_characteristics\], RB$M$-estimation i) applies to models that are at least partially-specified; ii) uses an analytical approximation to the bias function that relies only on derivatives of the contributions to the estimating functions; iii) does not depend on the original estimator; and iv) does not require the computation of any expectations. By relying only on derivatives of the contributions to the estimating functions, the new method is typically easier to implement for arbitrary models than other popular bias-reduction methods that require either resampling or the evaluation of moments of products of log-likelihood derivatives. In fact, automatic differentiation can be used to develop generic implementations of the new method whose only required input is an implementation of the contributions to the estimating functions. The GEEBRA Julia package (<https://github.com/ikosmidis/GEEBRA.jl>) by the Authors is a proof-of-concept of such an implementation.

If the estimating functions are the components of the gradient of an objective function, as is the case in maximum likelihood and maximum composite likelihood estimation, then, we show that bias reduction can always be achieved by the maximization 