The performance, in terms of coverage and expected length, of the model averaged tail area (MATA) confidence interval, proposed by Turek & Fletcher (2012, Computational Statistics & Data Analysis, 56, 2809–2815), depends greatly on the data-based model weights used in its construction. We generalise the computationally convenient exact formulae due to Kabaila, Welsh & Abeysekera (2016, Scandinavian Journal of Statistics, 43, 35–48) for the coverage and expected length of this confidence interval for two nested linear regression models to the case of two or more nested linear regression models. This permits the numerical assessment of the performance, in terms of coverage probability and scaled expected length, of the MATA confidence interval for any given data-based model weights in the context of three or more nested linear regression models. We illustrate this numerical assessment of performance of the MATA confidence interval, for model weights based on any given Generalised Information Criterion, in the context of three nested linear regression models using the real life ‘Cholesterol’ data. This provides a very informative further exploration of the influence of these model weights on the performance of this confidence interval.

中文翻译：

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嵌套线性回归模型中的模型平均尾部面积置信区间

Turek & Fletcher (2012,计算统计与数据分析, 56, 2809–2815)提出的模型平均尾部面积 (MATA) 置信区间在覆盖率和预期长度方面的性能很大程度上取决于数据 -基于其构造中使用的模型权重。我们将 Kabaila、Welsh 和 Abeysekera（2016 年，斯堪的纳维亚统计杂志，43, 35–48）的计算方便的精确公式推广到两个嵌套线性回归模型的该置信区间的覆盖范围和预期长度到两个或更多嵌套的线性回归模型。这允许在三个或更多嵌套线性回归模型的背景下，对任何给定的基于数据的模型权重的 MATA 置信区间的性能（覆盖概率和缩放预期长度）进行数值评估。我们在使用现实生活中“胆固醇”数据的三个嵌套线性回归模型的背景下，对基于任何给定广义信息准则的模型权重的 MATA 置信区间性能进行数值评估。这为进一步探索这些模型权重对该置信区间性能的影响提供了非常丰富的信息。