Minimax estimation of the expected conditional covariance under bounds on the covariate density
协变量密度有界条件下期望条件协方差的极小极大估计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：摘要明确将期望条件协方差用于治疗效应估计，但未提供具体因果识别设计。
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…
关注这篇论文的作者
协变量密度有界条件下期望条件协方差的极小极大估计
- 研究问题
- 协变量密度未知且仅有上下界时，期望条件协方差能够估计到何种精度，条件均值估计误差带来的偏差如何降低？
- 方法与思路
- 作者提出无需估计协变量密度的多分辨率估计量，分析有界响应和粗糙回归函数下的极小极大速率，并进行实验比较。
- 材料陈述的贡献
- 摘要称确定了优于既有猜测速率的次多项式改进，估计量距最优速率仅差对数因子，实验中可降低均方误差。
- 阅读关注点
- 应核对函数类和密度界的定义、速率上下界、次多项式改进的形式，以及偏差校正如何联系治疗效应估计。
- 阅读边界
- 材料是arXiv预印本v1，不能据此声称已经同行评审或期刊接收；具体正则条件、速率表达和实验细节未说明。
原文摘要
In many scientific studies, evaluating the association between two responses requires adjusting for shared covariates. The expected conditional covariance measures this adjusted association and is used in conditional independence testing and treatment effect estimation. Researchers often estimate it using fitted conditional means, but removing the bias caused by the estimation errors of these conditional means remains a difficult task. This difficulty can increase when the true covariate density is unknown and restricted only by known upper and lower bounds. In this article, we study how accurately the expected conditional covariance can be estimated under these density bounds. We propose a multiresolution estimator that reduces bias without estimating the density. Theoretical results show that, for bounded responses and rough regression functions, an unknown density slows the optimal worst-case rate by a power of sample size compared with a known density. We establish that the optimal rate under density bounds alone strictly improves upon the previously conjectured polynomial rate by a sub-polynomial factor, resolving a long-standing conjecture. Our estimator attains this rate up to a logarithmic factor. Through simulations and a real data resampling experiment on diamonds, we show that our method can yield smaller mean squared errors than standard uncorrected estimators.