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

• Activity Number: 183
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 10:30 AM to 12:20 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Hsun-chih Kuo*+
• Companies: National Chengchi University
• Keywords: Constrained MLE ; Local odds ratio Ordering ; Lagrangian.

Abstract

When natural odds ratio ordering exists in a contingency table, it is desirable to incorporate the natural ordering into estimatation of the cell probability. In this study, we intent to estimate the constrained MLE of the cell probabilities of a contingency table under local odds ratio constraints. We will consider four approaches: (1) convex optimization type of Lagrangian approach, (2) penalized Lagrangian approach modified from the first approach, (3) iterative algorithm that solves one local odds ratio constraint at a time, and (4) an approach to identify the ACTIVE local odds ratio constraints first and then utilize the closed-form solution to solve constrained MLE for these ACTIVE cells. The constrained MLE of the cell probabilities obtained from aforementioned four methods will be compared and discussed.