Designing optimal estimators for fish stock assessment

Many estimation procedures are used in the provision of fisheries stock assessment advice. Most procedures use estimators that have optimal large-sample characteristics, but these are often applied to small-sample data sets. In this paper, a minimum integrated average expected loss (MIAEL) estimation procedure is presented. By its design a MIAEL estimator has optimal characteristics for the type of data it is applied to, given that the model assumptions of the particular problem are satisfied. The estimation procedure is developed within a decision-theoretic framework and illustrated with a Bernoulli and a fisheries example. MIAEL estimation is related to optimal Bayes estimation, as both procedures seek an estimator that minimizes an integrated loss function. In most fisheries applications a global MIAEL estimator will be difficult to determine, and a MIAEL estimator will need to be found within a given class of estimators. "Squared f-error," a generalization of the common squared error loss function is defined. It is shown that an estimator can be improved (for a given squared f-error loss function) by using its best linear transformation which is the MIAEL estimator within the class of linear transformations (in f space).