Is it useful to know a nuisance parameter?

For parametric estimation in the presence of nuisance parameters, we show how to assess the usefulness of knowing the nuisance parameters from a classical as well as from a Bayesian point of view. In a recently published paper(Gini, 1996), it was claimed that exploitation of knowing a nuisance parameter could be disadvantageous in a mean squared error (MSE) sense, if biased estimators are used. This conclusion is misleading, since in (Gini, 1996) the MSEs of the maximum likelihood (ML) estimators with and without knowing the value of a nuisance parameter were compared, but the ML estimator is unsuitable to fully exploit the knowledge about the nuisance parameter with respect to the MSE. For clarification, we investigate just the same example as in (Gini, 1996). We show that optimal exploitation of the knowledge about the involved nuisance parameter decreases the minimum mean squared error, as intuition expects. (C) 1998 Elsevier Science B.V. All rights reserved.