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首页> 外文期刊>Journal of statistical computation and simulation >Generalized simultaneous confidence regions for regression coefficients and their ratios
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Generalized simultaneous confidence regions for regression coefficients and their ratios

机译：回归系数及其比率的广义同时置信区域

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This study constructs a simultaneous confidence region for two combinations of coefficients of linear models and their ratios based on the concept of generalized pivotal quantities. Many biological studies, such as those on genetics, assessment of drug effectiveness, and health economics, are interested in a comparison of several dose groups with a placebo group and the group ratios. The Bonferroni correction and the plug-in method based on the multivariate-t distribution have been proposed for the simultaneous region estimation. However, the two methods are asymptotic procedures, and their performance in finite sample sizes has not been thoroughly investigated. Based on the concept of generalized pivotal quantity, we propose a Bonferroni correction procedure and a generalized variable (GV) procedure to construct the simultaneous confidence regions. To address a genetic concern of the dominance ratio, we conduct a simulation study to empirically investigate the probability coverage and expected length of the methods for various combinations of sample sizes and values of the dominance ratio. The simulation results demonstrate that the simultaneous confidence region based on the GV procedure provides sufficient coverage probability and reasonable expected length. Thus, it can be recommended in practice. Numerical examples using published data sets illustrate the proposed methods.
机译：本研究基于广义枢轴量的概念，为线性模型系数及其比率的两种组合构造了一个同时置信区域。许多生物学研究，例如遗传学，药物疗效评估和健康经济学方面的研究，都对将几个剂量组与安慰剂组以及组比率进行比较感兴趣。提出了基于多重t分布的Bonferroni校正和插入方法用于同时区域估计。但是，这两种方法是渐近程序，并且它们在有限样本量中的性能尚未得到充分研究。基于广义枢纽量的概念，我们提出了Bonferroni校正程序和广义变量（GV）程序来构造同时置信区域。为了解决优势比的遗传问题，我们进行了模拟研究，以实证研究样本大小和优势比值的各种组合的方法的概率覆盖率和预期长度。仿真结果表明，基于GV过程的同时置信区间可提供足够的覆盖概率和合理的预期长度。因此，可以在实践中推荐它。使用已公开数据集的数值示例说明了所提出的方法。

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