2026-09-20T23:25:04Zhttps://krex.k-state.edu/server/oai/request

oai:krex.k-state.edu:2097/186832026-09-02T15:50:56Zcom_2097_1col_2097_4

Bai, Xiuqin 2014-11-18T17:11:22Z 2014-11-18T17:11:22Z 2014-11-18 2014 December http://hdl.handle.net/2097/18683 This proposal contains two projects that are related to robust mixture models. In the robust project, we propose a new robust mixture of regression models (Bai et al., 2012). The existing methods for tting mixture regression models assume a normal distribution for error and then estimate the regression param- eters by the maximum likelihood estimate (MLE). In this project, we demonstrate that the MLE, like the least squares estimate, is sensitive to outliers and heavy-tailed error distributions. We propose a robust estimation procedure and an EM-type algorithm to estimate the mixture regression models. Using a Monte Carlo simulation study, we demonstrate that the proposed new estimation method is robust and works much better than the MLE when there are outliers or the error distribution has heavy tails. In addition, the proposed robust method works comparably to the MLE when there are no outliers and the error is normal. In the second project, we propose a new robust mixture of linear mixed-effects models. The traditional mixture model with multiple linear mixed effects, assuming Gaussian distribution for random and error parts, is sensitive to outliers. We will propose a mixture of multiple linear mixed t-distributions to robustify the estimation procedure. An EM algorithm is provided to and the MLE under the assumption of t- distributions for error terms and random mixed effects. Furthermore, we propose to adaptively choose the degrees of freedom for the t-distribution using profile likelihood. In the simulation study, we demonstrate that our proposed model works comparably to the traditional estimation method when there are no outliers and the errors and random mixed effects are normally distributed, but works much better if there are outliers or the distributions of the errors and random mixed effects have heavy tails. Doctor of Philosophy Doctoral Department of Statistics Kun ChenWeixin Yao en_US Kansas State University © the author. This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). http://rightsstatements.org/vocab/InC/1.0/ Least square estimation EM algorithm Linear mixed models Mixture models Multivariate distribution Robust estimation Statistics (0463) Robust mixtures of regression models Dissertation open.access