Constrained Maximum Likelihood Estimation of Cell Probabilities Under Local Odds Ratio Constraints

摘要

When natural odds ratio ordering exists in a contingency table, it is desirable to incorporate the natural ordering into estimation of the cell probability in a contingency table. In this study, the constrained MLEs of the cell probabilities under local odds ratio constraints are studied. A lagrangian multiplier approach equipped with the Matrix Rule is considered. In addition, an iterative algorithm is also proposed to find the constrained MLE. The proposed two approaches based on the constrained MLEs of cell probabilities are compared with likelihood ratio ordering approach. It is found that all three approaches give identical solution, but the proposed approaches can be extended to more general settings.