Abstract:
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Data transformation and weighted least squares have been widely used to handle the problems of heteroscedasticity and non-normality in regression models. When a single transformation cannot be found to correct both, the data are usually transformed to induce normality and subsequently analyzed using weighted least squares. The search for such a transformation (if it does exit) for data masked by heterogeneous variances is, however, generally not straightforward. The present paper argues that it is considerably simpler to apply data transformation to eliminate the dependence of dispersion on the mean and then model the distribution of residuals parametrically. A recently proposed general class of probability distributions is used for modeling the error distributions in the new approach. Estimation and statistical inferences are then studied for the proposed parametric model. Numerical examples are used to demonstrate the practical usefulness of the proposed method.
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