Conditioning to reduce the sensitivity of general estimating functions to nuisance parameters

A conditional method is presented that renders an estimating function insensitive to nuisance parameters. The approach is a generalisation of the conditional score method to a general estimating function context and does not require complete specification of the probability model. We exploit the informal relationship between general estimating functions and score functions to derive simple generalisations of sufficient and partially ancillary statistics, referred to as G-sufficient and G-ancillary statistics, respectively. These two types of statistic are defined in a manner that does not require complete knowledge of the probability model and thus are more suitable for use with estimating functions. If we condition on a G-sufficient statistic for the nuisance parameters, the resulting conditional estimating function is insensitive to nuisance parameters and in particular achieves the plug-in unbiasedness property. Furthermore, if the conditioning argument is also G-ancillary for the parameters of interest, then the conditional estimating function possesses an attractive optimality property.