# What is an approximate ancillary statistic?

In the article Assessing the Accuracy of the Maximum Likelihood Estimator: Observed Versus Expected Fisher Information the authors use the expression "approximate ancillary statistic". This expression is used in a lot of others articles. Anyone know's the definition of approximate ancillary statistics?

A statistic $a$ is approximately ancillary for the estimation of $\theta$ if the asymptotic distribution of $a$ is free of $\theta$
So, it allows you to condition on statistics that are weakly associated with $\theta$ as long as this dependence approaches zero in some suitable sense.