Nobuhiro Taneichi, Yuri Sekiya, Jun Toyama

We consider logistic regression models in which the response variables are measured on a binary scale. We also consider a class of statistics which is based on ϕ-divergence as a goodness-of-fit test statistics for the model. The class of statistics include the statistics based on power divergence family as a special case. Well known Pearson's chi-square statistic and deviance (log likelihood ratio statistic) are included in power divergence family. All members of ϕ-divergence statistics have the limiting chi-square distribution assuming a certain condition under null hypothesis that logistic regression model is correct.

In this announcement, we construct and propose transformed ϕ-divergence statistics that improve the speed of convergence to the chi-square limiting distribution on the basis of the asymptotic expansion for lower probability of ϕ-divergence statistics. In order to investigate performance of the transformed statistic, we consider power divergence family of statistic as an example of ϕ-divergence family of statistic. Then, we numerically compare the speed of convergence of the transformed power divergence statistics with the original power divergence statistics. Furthermore, we also compare the power of the test based on transformed power divergence statistics with that of the test based on the original power divergence statistics.

**Keywords:** Asymptotic expansion; ϕ-divergence statistic; Logistic regression model; Transformed statistic

**Biography:** Place of birth: Hokkaido, Japan

1980: B.S., Mathematics, Hokkaido University

1987: Master of Engineering, Hokkaido University

1995: Doctor of Engineering, Hokkaido University

2001: Professor, Obihiro University of Agriculture and Veterinarty Medicine

2006: Professor, Department of Mathematics and Computer Science, Kagoshima University

Research Interest: Multivariate Analysis, Categorical Data Analysis, Asymptotic Theory.