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Statistical analysis reveals maximum likelihood sensitivity to variance misspecification in heteroscedastic linear models, highlighting greater generalized least squares robustness.
We consider a linear model with normally distributed but heteroscedastic errors. When the error variances are functionally related to the regression parameter, one can use either maximum likelihood or generalized least squares to estimate the regression parameter. We show that likelihood is more sensitive to small misspecifications in the functional relationship between the error variances and the regression parameter.
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Carroll et al. (1982) studied this question.
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