论文标题
强大的经验贝叶斯置信区间
Robust Empirical Bayes Confidence Intervals
论文作者
论文摘要
我们在正常手段问题中构建强大的经验贝叶斯置信区间（EBCI）。间隔以通常的线性经验贝叶斯估计量为中心，但使用关键值来收缩。在违反此假设时，假定平均值的正态分布的参数EBCI（Morris，1983b）可能会大大秘密。相反，无论均值分布如何，我们的EBCIS控制覆盖范围，同时在平均值确实是高斯时保持与参数EBCIS的长度。如果将手段视为固定的，我们的EBCIS具有平均覆盖范围保证：在每种手段的$ N $ EBCIS中，覆盖范围的平均值至少为$1-α$。我们的经验应用考虑了美国社区对代际移动性的影响。
We construct robust empirical Bayes confidence intervals (EBCIs) in a normal means problem. The intervals are centered at the usual linear empirical Bayes estimator, but use a critical value accounting for shrinkage. Parametric EBCIs that assume a normal distribution for the means (Morris, 1983b) may substantially undercover when this assumption is violated. In contrast, our EBCIs control coverage regardless of the means distribution, while remaining close in length to the parametric EBCIs when the means are indeed Gaussian. If the means are treated as fixed, our EBCIs have an average coverage guarantee: the coverage probability is at least $1 - α$ on average across the $n$ EBCIs for each of the means. Our empirical application considers the effects of U.S. neighborhoods on intergenerational mobility.
