The EM Algorithm And Its Application To Contaminated Model

In this paper, we introduce the basic definition of the EM algorithm and we also introduce GEM and ECM algorithm which develop from EM algorithm. We explain the EM algorithm's property, consider the problem of convergence in two ways that are likelihood and parameter and give the convergence condition respective. We also explain the connection between EM algorithm's convergence and missing information.The application of the EM algorithm is very wide. In this paper we use EM algorithm to solve the parameters' estimation of the contaminated model. In fact, the data is inexistence which obey one distribution strictly. J.W.Tukey advance a distribution mode which close to fact, saying contaminated distribution. It can denote as G=(1-v)F+vH, F is principal distribution and H is contaminated distribution. Now, the research about the contaminated model is one of the most important field in statistics. In this paper we discuss the regression model of one dimension contaminated data, using EM algorithm and Gibbs sampling to solve the MLE of regression parameters and contaminated parameter of the contaminated data. At the beginning, we also suppose the variances are known, using EM algorithm and Gibbs sampling to solve the estimation at this situation. At last we can extend EM algorithm to the condition of the unknown of variances and find the satisfactory result.