Improvement of inference for generalized linear model with binary response.

从两个角度改进了二元响应广义线性模型的推论。一方面，通过对Aranda-Ordaz提出的一个连接函数族的推广，构造了参数连接函数族。通过环族，我们可以选择一个模型，可以拟合各种数据。另一方面，我们构造了一个改进的转换统计量，它是基于拟合优度检验统计量的近似，通过使用Edgeworth展开。虽然基于变换后的统计量的检验功效与原始统计量的检验功效相差不大，但变换后的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.