In stating the results of their research, scientists usually want to publish narrow confidence intervals because they give precise estimates of the effects of interest. In many cases, the researcher would want to use the narrowest interval that maintains the desired coverage probability. In this manuscript, we propose a new method of finding confidence intervals that are often narrower than traditional confidence intervals for any individual parameter in a linear model if the errors are from a skewed distribution or from a long-tailed symmetric distribution. If the errors are normally distributed, we show that the width of the proposed normal scores confidence interval will not be much greater than the width of the traditional interval. If the dataset includes predictor variables that are uncorrelated or moderately correlated then the confidence intervals will maintain their coverage probability. However, if the covariates are highly correlated, then the coverage probability of the proposed confidence interval may be slightly lower than the nominal value. The procedure is not computationally intensive and an R program is available to determine the normal scores 95% confidence interval. Whenever the covariates are not highly correlated, the normal scores confidence interval is recommended for the analysis of datasets having 50 or more observations.

中文翻译：

---

一种使用正态分数变换来减小置信区间宽度的方法

在陈述他们的研究结果时，科学家们通常希望发布狭窄的置信区间，因为他们给出了对感兴趣的影响的精确估计。在许多情况下，研究人员会希望使用维持所需覆盖概率的最窄区间。在这份手稿中，我们提出了一种新方法，如果误差来自偏态分布或长尾对称分布，则该方法通常比线性模型中任何单个参数的传统置信区间更窄。如果误差是正态分布的，我们表明建议的正态分数置信区间的宽度不会比传统区间的宽度大很多。如果数据集包含不相关或适度相关的预测变量，则置信区间将保持其覆盖概率。但是，如果协变量高度相关，则建议的置信区间的覆盖概率可能会略低于标称值。该过程不是计算密集型的，并且可以使用 R 程序来确定正常分数的 95% 置信区间。每当协变量不高度相关时，建议使用正态分数置信区间来分析具有 50 个或更多观测值的数据集。该过程不是计算密集型的，并且可以使用 R 程序来确定正常分数的 95% 置信区间。每当协变量不高度相关时，建议使用正态分数置信区间来分析具有 50 个或更多观测值的数据集。该过程不是计算密集型的，并且可以使用 R 程序来确定正常分数的 95% 置信区间。每当协变量不高度相关时，建议使用正态分数置信区间来分析具有 50 个或更多观测值的数据集。