Statistica Sinica 14(2004), 283-295

THE MAXIMUM LIKELIHOOD ESTIMATES OF EXPECTED

FREQUENCIES UNDER THE LOOP ORDER

Ning-Zhong Shi and Shu-Rong Zheng

Northeast Normal University and Jilin University

Abstract: In this paper, we study the maximum likelihood estimates (MLEs) of expected frequencies under a loop order restriction in an $I \times J$ contingency table. Some properties of the MLEs are given and an algorithm for computing the MLEs is detailed. The proposed methods are illustrated by using the data from Wing (1962).

Key words and phrases: Expected frequency, Kuhn-Tucker condition, local odds ratio, loop order, MLE.