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Abstract:
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The presence of heteroscedasticity poses unique challenges: first, non-constant variance must be accurately detected; and second, usual methods that assume constant variance must be adjusted to account for the more complex variance structure. After a brief review of current approaches, we demonstrate properties and performance of mixture g priors for coefficients under a variety of priors for variances in the heteroscedastic case. We will analyze both simulated and real-world data sets to illustrate the ability to detect heteroscedasticity and estimate parameters using the two-way factorial layout as a case study. Finally, model averaging-based extensions of the selection procedures will be motivated to allow inference on model parameters in the presence of model uncertainty.
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