Robust multivariate mixture regression models

dc.contributor.authorLi, Xiongya
dc.description.abstractIn this dissertation, we proposed a new robust estimation procedure for two multivariate mixture regression models and applied this novel method to functional mapping of dynamic traits. In the first part, a robust estimation procedure for the mixture of classical multivariate linear regression models is discussed by assuming that the error terms follow a multivariate Laplace distribution. An EM algorithm is developed based on the fact that the multivariate Laplace distribution is a scale mixture of the multivariate standard normal distribution. The performance of the proposed algorithm is thoroughly evaluated by some simulation and comparison studies. In the second part, the similar idea is extended to the mixture of linear mixed regression models by assuming that the random effect and the regression error jointly follow a multivariate Laplace distribution. Compared with the existing robust t procedure in the literature, simulation studies indicate that the finite sample performance of the proposed estimation procedure outperforms or is at least comparable to the robust t procedure. Comparing to t procedure, there is no need to determine the degrees of freedom, so the new robust estimation procedure is computationally more efficient than the robust t procedure. The ascent property for both EM algorithms are also proved. In the third part, the proposed robust method is applied to identify quantitative trait loci (QTL) underlying a functional mapping framework with dynamic traits of agricultural or biomedical interest. A robust multivariate Laplace mapping framework was proposed to replace the normality assumption. Simulation studies show the proposed method is comparable to the robust multivariate t-distribution developed in literature and outperforms the normal procedure. As an illustration, the proposed method is also applied to a real data set.en_US
dc.description.advisorWeixing Songen_US
dc.description.degreeDoctor of Philosophyen_US
dc.description.departmentDepartment of Statisticsen_US
dc.publisherKansas State Universityen
dc.subjectFinite mixturesen_US
dc.subjectMultivariate regressionen_US
dc.subjectRobust estimationen_US
dc.subjectMultivariate Laplace distributionen_US
dc.subjectEM algorithmen_US
dc.subjectQuantitative trait locien_US
dc.titleRobust multivariate mixture regression modelsen_US


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