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Simultaneous confidence intervals of estimable functions based on quasi-likelihood in generalized linear models for over-dispersed data
Journal of Statistical Computation and Simulation ( IF 1.2 ) Pub Date : 2020-08-19 , DOI: 10.1080/00949655.2020.1807548
Bo Li 1
Affiliation  

Two major problems besetting count data analysis in multiple comparisons are over-dispersion and violation of distributional assumptions of real data. In this article, we describe the simultaneous confidence interval method to inference a collection of estimable functions in generalized linear models based on quasi-likelihood estimation. We assume that the independent observations have the variance proportional to a given function of the mean. We define the pivotal quantities in an asymptotic sense. We derive the joint limiting distribution of the pivotal quantities and the asymptotic distribution of the maximum modulus statistic. In the presence of over-dispersion, large-sample approximation method is shown to be liberal in multiple comparisons. We propose a percentile-t bootstrap method based on Pearson residuals as a robust alternative. It shows that the proposed method outperforms large-sample approximation method in the spirit of attaining the overall coverage probability, even when the working variance-mean structure moderately deviates from the real structure of the underlying distribution.

中文翻译:

过度分散数据广义线性模型中基于拟似然的可估计函数的同时置信区间

在多重比较中困扰计数数据分析的两个主要问题是过度分散和违反真实数据的分布假设。在本文中,我们描述了在基于拟似然估计的广义线性模型中推断一组可估计函数的同时置信区间方法。我们假设独立观测的方差与给定的均值函数成正比。我们以渐近的方式定义关键量。我们推导出关键量的联合极限分布和最大模量统计量的渐近分布。在存在过度分散的情况下,大样本近似方法在多重比较中表现出自由。我们提出了一种基于 Pearson 残差的百分位数 t 引导法作为一种稳健的替代方法。
更新日期:2020-08-19
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