Bias in Nonlinear Regression.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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This document investigates the biases of the residuals and the maximum likelihood parameters estimates from standard, normal-theory nonlinear regression models. Emphasis is placed on determining the influence of individual cases on the biases and on understanding how the residual biases can affect the usefulness of standard diagnostic methods. It is shown that the various bias expressions in the literature are equivalent, that the biases in nonlinear regression can be studied usefully in the context of linear regression, and that diagnostic plots using residuals can be misleading because of substantial residual biases. For a class of partially nonlinear models, it is shown that the maximum intrinsic curvature is closely related to the residual expectations. Finally, the model associated with power transformations of single explanatory variables in linear regression is investigated in further detail and several numerical illustrations are presented. Author
- Statistics and Probability