Estimating a percent reduction in load

Abstract

This article extends the work of Cohn et al. [1989] on estimating constituent loads to the problem of estimating a percent reduction in load. Three estimators are considered: the maximum likelihood (MLE), a “bias‐corrected” maximum likelihood (BCMLE), and the minimum variance unbiased (MVUE). In terms of root‐mean‐square error, both the MVUE and BCMLE are superior to the MLE, and for the cases considered here there is no appreciable difference between the MVUE and the BCMLE. The BCMLE is constructed from quantities computed by most regression packages and is therefore simpler to compute than the MVUE (which involves approximating an infinite series). All three estimators are applied to a case study in which an agricultural tax in the Everglades agricultural area is tied to an observed percent reduction in phosphorus load. For typical hydrological data, very large sample sizes (of the order of 100 observations each in the baseline period and after) are required to estimate a percent reduction in load with reasonable precision.