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A0486
Title: Improved $\phi$-divergence test statistics based on minimum $\phi^{*}$-divergence estimator for GLIMs of binary data Authors:  Nobuhiro Taneichi - Kagoshima University (Japan) [presenting]
Yuri Sekiya - Hokkaido University of Education (Japan)
Jun Toyama - The Institute for the Practical Application of Mathematics (Japan)
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, $\phi$-divergence family of goodness-of-fit test statistics $C_{\phi \phi^{*}}$ which is based on minimum $\phi^{*}$-divergence estimator is considered. Family of statistics $C_{\phi \phi^{*}}$ includes a power divergence family of statistics $R^{a,b}$ which is based on minimum power divergence estimator. The derivation of an expression of continuous term of asymptotic expansion for the distribution of $C_{\phi \phi^{*}}$ under the null hypothesis is shown. Using the expression, a transformed $C_{\phi \phi^{*}}$ statistic that improves the speed of convergence to the chi-square limiting distribution of $C_{\phi \phi^{*}}$ is obtained. In the case of $R^{a,b}$, it is numerically shown that the transformed statistics perform much better than the original statistics and it is also numerically shown that power of the transformed statistics is almost the same as that of the original statistics.