Estimator bias in a lake phosphorus model with observation error

Abstract

We investigated observation-error-induced parameter bias using least squares and Stein-corrected least squares estimators in a model for predicting lake phosphorus. The Stein-corrected estimator performed better than the uncorrected estimator from bias and 'closeness' perspectives, though the corrected estimator was still biased. Examination of the model structure revealed that parameter bias is strongly related to both the parameter space and sample space. Additionally, the model is robust to parameter bias over a large portion of the sample and parameter space, indicating that this model may be particularly useful for estimation and prediction. Analogous structure in other models could be an important consideration for model selection