ABSTRACT

It is now nearly 50 years since Neyman and Scott (1948) established that maximum likelihood estimation could have severe failings when estimating a parameter of interest in the presence of many nuisance parameters. In

particular, they demonstrated that with infinitely many nuisance parameters, the maximum likelihood estimator could fail to be consistent, and even if consistent, could fail to be the most efficient estimator. We return to this problem to show that with a little mathematical prodding, one can derive simple and meaningful ways of assessing the statistical impact of nuisance parameters.