IS IT USEFUL TO KNOW A NUISANCE PARAMETER

For parametric estimation in the presence of nuisance parameters, we s how how to assess the usefulness of knowing the nuisance parameters fr om a classical as well as from a Bayesian point of view. In a recently published paper(Gini, 1996), it was claimed that exploitation of know ing a nuisance parameter could be disadvantageous in a mean squared er ror (MSE) sense, if biased estimators are used. This conclusion is mis leading, 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 th e 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 involve d nuisance parameter decreases the minimum mean squared error, as intu ition expects. (C) 1998 Elsevier Science B.V. All rights reserved.