Confidence Intervals with More Power to Determine the Sign: Two Ends Constrain the Means
更有能力判定均值符号的置信区间：两端约束均值AI 解读 ↓
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更有能力判定均值符号的置信区间：两端约束均值
- 研究问题
- 对连续、单峰、对称变量的均值，如何设计双侧置信区间，使较小观测也能判定符号，并权衡不同参数区域的长度？
- 方法与思路
- 作者提出两族非等变双侧区间，分别修改Pratt构造与常规对称区间端点，并提供正态和t统计量的实施常数。
- 材料陈述的贡献
- 摘要称两族区间在观测较小时更短且更易判定符号，无须预定方向；同时明确指出部分参数区域的期望长度会增加。
- 阅读关注点
- 应核对覆盖率保证、非等变构造的具体端点规则，以及符号判定能力与区间长度在不同均值区域中的权衡。
- 阅读边界
- 依据版本未注明的 OpenAlex 索引摘要。所述优势依赖模型与参数区域，不能认定区间处处更短；诉讼例子的具体结果未提供。
原文摘要
We present two new families of two-sided nonequivariant confidence intervals for the mean θ of a continuous, unimodal, symmetric random variable. Compared with the conventional symmetric equivariant confidence interval, they are shorter when the observation is small, and restrict the sign of θ for smaller observations. One of the families, a modification of Pratt's construction of intervals with minimal expected length when θ = 0, is longer than the conventional symmetric interval when |X| is large and has longer expected length when |θ| is large. The other family gives the conventional symmetric interval when |X| is large, with a change to the proximal endpoint when |X| is small. Its expected length is smaller than that of the conventional symmetric interval when |θ| is small, larger for an intermediate range of |θ|, and approaches that of the conventional interval for large |θ|. This slight modification of the conventional two-sided interval has most of the power advantage of a one-sided interval, but short length. Neither procedure requires that a preferred direction be specified in advance. The constants that determine the procedures can be found for symmetrically distributed statistics using any software package that includes the cumulative distribution function and inverse cumulative distribution function of the statistic, along with a root finder. We present tables of constants needed to apply the procedures for normally and t-distributed test statistics, and give an application to employment discrimination litigation.