Shi, Ning-Zhong; Zheng, Shu-Rong The maximum likelihood estimates of expected frequencies under the loop order. (English) Zbl 1035.62057 Stat. Sin. 14, No. 1, 283-295 (2004). Summary: 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 data of J. K. Wing [Brit. J. Soc. Clin. Psychol. 1, 38–51 (1962)]. MSC: 62H17 Contingency tables 62F30 Parametric inference under constraints 62F10 Point estimation 65C60 Computational problems in statistics (MSC2010) Keywords:expected frequency; Kuhn-Tucker condition; local odds ratio; loop order; MLE; maximum likelihood PDFBibTeX XMLCite \textit{N.-Z. Shi} and \textit{S.-R. Zheng}, Stat. Sin. 14, No. 1, 283--295 (2004; Zbl 1035.62057)