Covariances in Multiplicative Estimates

Abstract

Multiplicative estimators, in which a quantity is calculated as the product of two or more estimated factors, are relatively common in fisheries work. Creel surveys and stock assessment data are two obvious examples. If the same multiplicative factor is used in several estimates, or if there is covariance between multiplicative factors, then covariances will be induced in the estimates produced. These covariances can be large in some instances. This paper reviews general results for the variance and covariance of products, provides estimators for the induced covariances in some common fisheries applications, and demonstrates the use of the estimators in some simplified examples.