Compound Estimation for Binomials
二项分布均值的复合估计AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
本页为预印本版本；arXiv 收录、作者填写的期刊信息以及作者既有发表经历，都不单独证明本篇已接收。作者发表记录按 OpenAlex 身份与完整姓名、本站覆盖期刊 ISSN 及正式卷期核对，只展示已核实例，档案仍可能误合并。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要核心是通用二项参数的复合决策与收缩理论，所列应用不足以明确对应某个计量细分。
反馈分类问题
正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
二项分布均值的复合估计
- 研究问题
- 在同时估计多个二项均值且样本量异质、均值较小时，如何跨任务借用信息降低平均误差，并避免依赖高斯近似？
- 方法与思路
- 作者在样本量和均值均固定的复合决策框架中，构造平均均方误差的近似 SURE，并研究机器学习辅助线性收缩估计。
- 材料陈述的贡献
- 摘要称建立所述收缩估计的渐近最优性、遗憾界和有效推断，直接处理二项观测，并展示单样本与双样本场景的应用。
- 阅读关注点
- 应核对近似风险估计的误差、收缩类及最优性参照对象，以及小样本量、低成功概率和异质样本量下的推断条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未给出风险界、渐近序列或数据结果，不能认定所有收缩方法均有保证。
原文摘要
Many applications involve estimating the mean of multiple binomial outcomes as a common problem -- assessing intergenerational mobility of census tracts, estimating prevalence of infectious diseases across countries, and measuring click-through rates for different demographic groups. The most standard approach is to report the plain average of each outcome. Despite simplicity, the estimates are noisy when the sample sizes or mean parameters are small. In contrast, the Empirical Bayes (EB) methods are able to boost the average accuracy by borrowing information across tasks. Nevertheless, the EB methods require a Bayesian model where the parameters are sampled from a prior distribution which, unlike the commonly-studied Gaussian case, is unidentified due to discreteness of binomial measurements. Even if the prior distribution is known, the computation is difficult when the sample sizes are heterogeneous as there is no simple joint conjugate prior for the sample size and mean parameter. In this paper, we consider the compound decision framework which treats the sample size and mean parameters as fixed quantities. We develop an approximate Stein's Unbiased Risk Estimator (SURE) for the average mean squared error given any class of estimators. For a class of machine learning-assisted linear shrinkage estimators, we establish asymptotic optimality, regret bounds, and valid inference. Unlike existing work, we work with the binomials directly without resorting to Gaussian approximations. This allows us to work with small sample sizes and/or mean parameters in both one-sample and two-sample settings. We demonstrate our approach using three datasets on firm discrimination, education outcomes, and innovation rates.