distribution function of the process that generated the data, ${{}B}_G({{}\theta}) = \expect_G(\hat{{}\theta} - {{}\theta})$ is the bias function, and $\bar{{}\theta}$ is the value that $\hat{{}\theta}$ is assumed to converge to in probability as information about ${{}\theta}$ increases, typically with the volume of the data. The need for approximating the solution of (\[bias\_equation\]) arises because, on one hand, $G$ is either unknown or the expectation with respect to $G$ is not available in closed form, and, on the other hand, the value of $\bar{{}\theta}$ is unknown.

Table \[br\_characteristics\] classifies prominent bias-reduction methods according to various criteria relating to their applicability and operation. Given the size of the literature on bias-reduction methods, we only cite key works that defined or greatly impacted the area.

Bias-reduction methods like the adjusted scores functions approach in @firth:1993, indirect inference in @gourieroux:1993, and iterated bootstrap in @kuk:1995 and @guerrier+dupuis-lozeron+etal:2019, assume that the model can be fully and correctly specified, in the sense that $G$ results from the assumed model for specific parameter values. That assumption allows to either have access to log-likelihood derivatives and expectations of products of those or to simulate from the model. In contrast, bias-reduction methods, like asymptotic bias correction [@efron:1975], bootstrap [@efron+tibshirani:1993; 