Maximum Likelihood Parameter Estimation For Multi-dimensional Normal Distribution Based On EM Algorithm

In this paper, we discuss the maximum likelihood parameter estimation for multi-dimensional normal distribution based on EM algorithm. We use a approximation method to get the solution of maximum likelihood estimation equations to deal with the difficulty in computing the M-step as a result of the high dimensions of the data. We estimate the complete data and missing data respectively and mix them by the weighted mean. Finally we use the algorithm to take a digital simulation to test the validity.This dissertation is organized as follows: In chapter 1, we introduce the applications and results of the EM algorithm in parameter estimation. In chapter2, we introduce the definition and properties of maximum likelihood estimation, multi-dimensional distribution and parameter estimation and the EM algorithm. In chapter 3, we study the maximum likelihood parameter estimation for multi-dimensional normal distribution based on EM algorithm. We use the idea of weighted mean when computing M-step and get an approximate estimation as an result. Finally we make a digital simulation to test the validity of the above method.