Inference in mixed models with a mixture of distributions and controlled heteroscedasticity

In the realm of mixed models, this article explores the estimation method for incorporating a mixture of distributions and addressing controlled heteroscedasticity. By relaxing the assumptions of normality and homoscedasticity, we introduce a more flexible approach to analyzing data. The article presents estimation techniques for variance components, estimable vectors, and cumulants, while also developing prediction intervals and prediction ellipsoids for future observations. A numerical example is employed to illustrate the method and compare it with traditional ANOVA and Bayesian estimation methods. The results demonstrate the superior flexibility and broader applicability of the proposed methods in diverse contexts. By extending the analysis beyond conventional assumptions, these approaches enhance the accuracy and robustness of statistical inference in mixed models.