Jin, Yinghua; Wu, Yaohua; Shao, Quanxi One-sided test based on \(\phi \)-divergence under log-linear models. (Chinese. English summary) Zbl 1424.62127 Acta Math. Appl. Sin. 41, No. 4, 497-510 (2018). Summary: One-sided test is an important part of hypothesis test theory. A kind of one-sided test for log-linear models under product-multinomial sampling is studied in this paper. Based on \(\phi \)-divergence and the restricted minimum \(\phi \)-divergence estimator (RM\(\phi\)DE), three families of statistics are proposed. All the three proposed statistics have identical asymptotic distribution as Chi-bar-square distribution, and include the likelihood ratio statistic and the Pearson statistic as special cases. These proposed statistics can be treated as a generalization of the results in existing literature with three improvements: the model in this paper is much wider than the saturated log-linear model they considered; the form of one-sided test is much more general than the likelihood ratio ordering test they constructed; and RM\(\phi\)DE used to construct these statistics is more general than the maximum likelihood estimator (MLE) they used. Real data analysis demonstrates the effect of these statistics. A simulation study shows that some members of the power-divergence family could act as superior alternatives to the likelihood ratio statistic and the Pearson statistic under finite sample sizes. MSC: 62J12 Generalized linear models (logistic models) 62F05 Asymptotic properties of parametric tests Keywords:one-sided test; \(\phi \)-divergence; product-multinomial sampling; log-linear model; chi-bar-square distribution PDFBibTeX XMLCite \textit{Y. Jin} et al., Acta Math. Appl. Sin. 41, No. 4, 497--510 (2018; Zbl 1424.62127)