Abstract
Generalized linear models of binary data including a logistic regression model and a probit model are considered. For testing the null hypothesis that the considered model is correct, the -divergence family of goodness-of-fit test statistics that is based on a minimum -divergence estimator is considered. The family of statistics includes a power divergence family of statistics that is based on a minimum power divergence estimator. The derivation of an expression of a continuous term of asymptotic expansion for the distribution of under the null hypothesis is shown. Using the expression, a transformed statistic that improves the speed of convergence to the chi-square limiting distribution of is obtained. In the case of , it is numerically shown that the transformed statistics usually perform better than the original statistics with respect to speed of convergence to the chi-square limiting distribution and it is also numerically shown that the power of the transformed statistics is almost the same as that of the original statistics.
Funding Statement
This research is partially supported by the Grants-in-aid for Scientific Research of Japan Society for the Promotion of Science (C) 24540133.
Citation
Nobuhiro Taneichi. Yuri Sekiya. Jun Toyama. "Improved transformation of -divergence goodness-of-fit test statistics based on minimum -divergence estimator for GLIM of binary data." SUT J. Math. 52 (2) 193 - 214, December 2016. https://doi.org/10.55937/sut/1483720971
Information