Improvement of inference for generalized linear model with binary response.

从两个角度改进了具有二元响应的广义线性模型的推论。一方面，我们通过扩展Aranda-Ordaz提出的链函数族来构造参数链函数族。通过链接族，我们可以选择一个可以拟合各种数据的模型。另一方面，我们利用Edgeworth展开构造了一种改进的变换统计量，该变换统计量是基于拟合优度检验统计量的近似。虽然基于变换统计量的检验能力与原始统计量相差不大，但变换统计量很好地提高了收敛到卡方分布的速度。

We improved the inference for generalized linear model with binary response from two kinds of view point. On the one hand, we constructed family of parametric link functions by extending family of a link function proposed by Aranda-Ordaz. By the family of links, we can choose a model that can be fitted various data. One the other hand, we constructed an improved transformed statistic which is based on an approximation of goodness-of-fit test statistic by using Edgeworth expansion. Though the power of the test based on the transformed statistic is not so different from that of original statistic, the transformed statistic improves the speed of convergence to chi-square distribution very well.