Master of Science / Department of Statistics / Weixin Yao / In this report, we investigate a robust estimation of the number of components in the mixture of regression models using trimmed information criterion. Compared to the traditional information criterion, the trimmed criterion is robust and not sensitive to outliers. The superiority of the trimmed methods in comparison with the traditional information criterion methods is illustrated through a simulation study. A real data application is also used to illustrate the effectiveness of the trimmed model selection methods.

Master of Science / Department of Statistics / Weixin Yao / Mixtures of factor analyzers have been popularly used to cluster the high dimensional data. However, the traditional estimation method is based on the normality assumptions of random terms and thus is sensitive to outliers. In this article, we introduce a robust estimation procedure of mixtures of factor analyzers using the trimmed likelihood estimator (TLE). We use a simulation study and a real data application to demonstrate the robustness of the trimmed estimation procedure and compare it with the traditional normality based maximum likelihood estimate.