A Note Of Multinomal Maximum Likelihood Estimation Under Ordered Restrictions And The EM Alogorithm

A frequently occurring problem is to find the maximum likelihood estimation(MLE) of p subject to p ∈ C(C P the probability vectors in R~k). The problem has been discussed by many authors and they mainly focused when p is restricted by linear constraints or log-linear constraints. In this paper, we construct the relationship between the the maximum likelihood estimation of p restricted by p ∈ C and EM algorithm and demonstrate that the maximum likelihood estimator can be computed through the EM algorithm(Dempster, Laird and Rubin(1977)).And then we will give a simple iterative algorithm based on the edges of C to compute the MLE of p ,which is applicable for both equality and inequality constraints.The second major content is the consideration to the marginal homogeneity of the square contingency table. Several examples are analyzed by the proposed method.