of an appropriately penalized version of the objective. This is in contrast to the method in @firth:1993 which does not always have a penalized likelihood interpretation; see, for example, @kosmidis+firth:2009, who derive a necessary and sufficient condition for the existence of bias-reducing penalized likelihood for generalized linear models. Moreover, it is shown that the bias-reducing penalized objective closely relates to information criteria for model selection based on the Kullback-Leibler divergence. The functions of the parameters and the data that are used for bias reduction and model selection differ only by a known scalar constant. These observations, establish, for the first time, a strong link between reduction of bias in estimation and model selection. It is also shown that the RB$M$-estimators have the same asymptotic distribution, hence the same asymptotic efficiency properties, as the original $M$-estimators, and we discuss inference and model selection with RB$M$-estimates.

Section \[modelling\_setting\] introduces notation and sets up the general modelling setting we consider and the assumptions underpinning the theoretical developments. Section \[sec:theory\] and Section \[empirical\_adjustments\] are devoted on the derivation of the bias-reducing, empirical adjustments to the estimating functions and the specification of their components. Section \[sec:inference\] shows that the asymptotic distribution of the RB$M$ estimator 