标题： 大规模未知异方差性下的估计 显示英文标题

标题： Large-Scale Estimation under Unknown Heteroskedasticity

摘要： 本文研究了在具有未知均值和方差的异质参数框架中的非参数经验贝叶斯方法。我们提供了扩展的Tweedie公式，这些公式用某些充分统计量的密度来表示（不可行的）异质参数的最优估计量，例如单元特定的均值或分位数。这些公式被用来提出可行版本，其几乎参数化的遗憾界为$(\log n)^\kappa / n$的数量级。这些估计量被用于教师增值的研究中，我们发现允许教师之间方差的异质性对于提供教师质量的最佳估计和检测低绩效教师至关重要。 显示英文摘要

摘要： This paper studies nonparametric empirical Bayes methods in a heterogeneous parameters framework that features unknown means and variances. We provide extended Tweedie's formulae that express the (infeasible) optimal estimators of heterogeneous parameters, such as unit-specific means or quantiles, in terms of the density of certain sufficient statistics. These are used to propose feasible versions with nearly parametric regret bounds of the order of $(\log n)^\kappa / n$. The estimators are employed in a study of teachers' value-added, where we find that allowing for heterogeneous variances across teachers is crucial for delivery optimal estimates of teacher quality and detecting low-performing teachers.