Heteroscedastic Nonlinear Regression

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Abstract
Several parameter estimation methods for dealing with heteroscedasticity in nonlinear regression are described. These include variations on ordinary, weighted, iteratively reweighted, extended. and generalized least squares. Some of these variations are new, and one of them in particular, modified extended iteratively reweighted least squares (MEIRLS), allows parameters of an assumed heteroscedastic variance model to be estimated with an adjustment for bias due to estimation of the regression parameters. The context of the discussion is primarily that of pharmacokinetic-type data, although an example is given involving chemical-reaction data. Using simulated data from 21 heteroscedastic pharmacokinetic-type models, some of the methods are compared in terms of mean absolute error and 95% confidence-interval coverage. From these comparisons, MEIRLS and the variations on generalized least squares emerge as the methods of choice.

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