Estimation in the Presence of Nuisance Parameters

We consider MVUE and median unbiased estimation in the presence of nuisance parameters. For several different situations sufficient assumptions are formulated guaranteeing that conditionality and marginalization principles lead to optimal estimators. We also discuss some related questions such as the maximality of ancillary statistics, completeness in markovian models, and a generalization of the independence of complete sufficient statistics and ancillary statistics due to Basu.