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Robust EM Algorithm For Mixed Linear Regression Models With Right Censored Data

Posted on:2017-01-10Degree:MasterType:Thesis
Country:ChinaCandidate:Y Q XingFull Text:PDF
GTID:2297330488996665Subject:Statistics
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Mixture models have been widely used in many files, including crop breeding, voice recognition, finding motif problem of biopolymer, face recognition, as a con-sequence, this models have been concerned by more and more researcher in recent years. As the most basic methods of parameter estimation, maximum likelihood esti-mation(MLE) and least squares estimate(LSE) naturally become the primary choice of the mixture model regression method. But, there are many computing problems when we estimate the parameters of mixture model using maximum likelihood estimation. Since1977, Dempster et al. calculated maximum likelihood estimates via the Expec-tation Maximization (EM) algorithm, the study of the mixed model has entered a new stage of development. But, with the development and application of the theory, new problem appeared because that real data is not so standard as the data in simulation experiment based on the model. When observations exist outliers or the errors term of mixture model follow some heavy-tailed distribution, estimate will strongly influ-enced by the outliers and the heavy tails. So the above two methods(MLE and LSE) become less effective. Then, many people make tremendous efforts to look for robust estimation method to estimate the parameter of mixture models. In fact, Neykov, Bai et al., Song et al. have already put forward some robust estimate methods of mixture models respectively. On this basis, this paper generalize the idea about robust regression for mixed linear models of Bai et al. to the situation with right censored data.The work of this thesis mainly include the following several aspects:Firstly, for the mixed linear regression model when there is no censored data, I introduce the traditional EM algorithm and Bai’s robust parameter estimation method by combining the thoughts of generalized maximum likelihood estimation (M-estimate) and the EM algorithm in the paper [3]. The next part is the innovations of my thesis, and in this part I extend the two parameter estimation methods to the situation with censored data respectively. On one hand, I use the EM algorithm to estimate the parameters of the mixed linear regression model when there is right censored data. On the other hand, by combining the thought of robust M-estimate and EM algorithm, I provide a robust EM type regression method for the mixed linear regression model with right censored data. Finally, it is identified that this two regression methods are all effective for the mixed linear regression model with right censored data through numerical simulation. Meanwhile, through comparing and analyzing, it is also well demonstrated that the proposed robust EM type method is more robust than the MLE and EM algorithm when there exist outliers and heavy tails.
Keywords/Search Tags:Mixture linear models, Right censored data, M-estimate, EM algorithm, Robust estimate, Outliers, Heavy-tailed distribution
PDF Full Text Request
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