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WATER RESOURCES RESEARCH, VOL. 41, W07003, doi:10.1029/2004WR003833, 2005

Estimating contaminant loads in rivers: An application of adjusted maximum likelihood to type 1 censored data

Timothy A. Cohn

U.S. Geological Survey, Reston, Virginia, USA


Abstract

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.

Received 22 November 2004; accepted 23 March 2005; published 6 July 2005.

Keywords: adjusted maximum likelihood estimation.

Index Terms: 1871 Hydrology: Surface water quality; 1869 Hydrology: Stochastic hydrology; 1862 Hydrology: Sediment transport (4558); 1873 Hydrology: Uncertainty assessment (3275); 1806 Hydrology: Chemistry of fresh water.

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Citation: Cohn, T. A. (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.