Robust multivariate mixture regression models

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dc.contributor.author Li, Xiongya
dc.date.accessioned 2017-12-11T15:38:02Z
dc.date.available 2017-12-11T15:38:02Z
dc.date.issued 2018-05-01 en_US
dc.identifier.uri http://hdl.handle.net/2097/38427
dc.description.abstract In 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.language.iso en_US en_US
dc.publisher Kansas State University en
dc.subject Finite mixtures en_US
dc.subject Multivariate regression en_US
dc.subject Robust estimation en_US
dc.subject Multivariate Laplace distribution en_US
dc.subject EM algorithm en_US
dc.subject Quantitative trait loci en_US
dc.title Robust multivariate mixture regression models en_US
dc.type Dissertation en_US
dc.description.degree Doctor of Philosophy en_US
dc.description.level Doctoral en_US
dc.description.department Department of Statistics en_US
dc.description.advisor Weixing Song en_US
dc.date.published 2018 en_US
dc.date.graduationmonth May en_US


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