The Equivalence of Generalized Least Squares and Maximum Likelihood Estimates in the Exponential Family

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Abstract
The method of iterative weighted least squares can be used to estimate the parameters in a nonlinear regression model. If the dependent variables are observations from a member of the regular exponential family, then under mild conditions it is shown that the IWLS estimates are identical to those obtained using the maximum likelihood principle. An application is provided to illustrate the results.

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