Abstract
An expression is given for the exact probability density function of the parameter values that maximize the likelihood of a statistical model, where the data generating model is allowed to differ from the estimation model. The density can be used to study the robustness of estimation of alternative hypothetical models. It is described for curved exponential families, then specifically for gamma distribution models and for nonlinear regression models. An example is given in the context of alternative models for data from the biochemical ELISA test method. Finally an indication is given of how a robustness index can be calculated to assess the effects of estimation of a common parameter vector under a wrong model.
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Hingley, P.J. (2004). Analytic Estimator Densities for Common Parameters under Misspecified Models. In: Hubert, M., Pison, G., Struyf, A., Van Aelst, S. (eds) Theory and Applications of Recent Robust Methods. Statistics for Industry and Technology. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7958-3_11
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DOI: https://doi.org/10.1007/978-3-0348-7958-3_11
Publisher Name: Birkhäuser, Basel
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