Estimating contaminant loads in rivers: An application of adjusted maximum likelihood to type 1 censored data
Article first published online: 6 JUL 2005
Copyright 2005 by the American Geophysical Union.
Water Resources Research
Volume 41, Issue 7, July 2005
How to Cite
2005), Estimating contaminant loads in rivers: An application of adjusted maximum likelihood to type 1 censored data, Water Resour. Res., 41, W07003, doi:10.1029/2004WR003833.(
- Issue published online: 6 JUL 2005
- Article first published online: 6 JUL 2005
- Manuscript Accepted: 23 MAR 2005
- Manuscript Revised: 14 MAR 2005
- Manuscript Received: 22 NOV 2004
- adjusted maximum likelihood estimation
 This paper presents an adjusted maximum likelihood estimator (AMLE) that can be used to estimate fluvial transport of contaminants, like phosphorus, that are subject to censoring because of analytical detection limits. The AMLE is a generalization of the widely accepted minimum variance unbiased estimator (MVUE), and Monte Carlo experiments confirm that it shares essentially all of the MVUE's desirable properties, including high efficiency and negligible bias. In particular, the AMLE exhibits substantially less bias than alternative censored-data estimators such as the MLE (Tobit) or the MLE followed by a jackknife. As with the MLE and the MVUE the AMLE comes close to achieving the theoretical Frechet-Cramér-Rao bounds on its variance. This paper also presents a statistical framework, applicable to both censored and complete data, for understanding and estimating the components of uncertainty associated with load estimates. This can serve to lower the cost and improve the efficiency of both traditional and real-time water quality monitoring.