arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2602.01595stat.MEmath.STstat.TH
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基于最小方差加权的数据驱动统一推断:一般连续处理模型

Data-Driven Uniform Inference for General Continuous Treatment Models via Minimum-Variance Weighting

School of Management and Economics, Chinese University of Hong Kong, Shenzhen(香港中文大学(深圳)经管学院);School of Mathematics and Statistics, University of Melbourne(墨尔本大学数学与统计学院);Center for Applied Statistics, Institute of Statistics & Big Data, Renmin University of China(中国人民大学统计学院大数据研究中心)

Chunrong Ai, Wei Huang, Zheng Zhang

AI总结:

本文提出了一种数据驱动的方法,通过最小方差加权估计一般连续处理模型的GDRF,并构建统一置信带。

摘要:

Ai等(2021)研究了一般剂量反应函数(GDRF)的估计问题,该函数包括平均剂量反应函数、分位数剂量反应函数以及其他剂量反应分布的期望值。他们将GDRF指定为仅依赖于处理状态的参数函数,并提出了使用最大熵方法估计加权函数的加权回归。本文将GDRF指定为仅依赖于处理状态的非参数函数,提出了一种加权局部线性回归来估计GDRF,并开发了用于构建统一置信带的自助法。我们提出了一种具有最小样本方差的稳定权重,同时消除了处理与混杂变量之间的样本关联性。所提出的权重具有闭式表达式,允许在自助抽样中高效计算。在某些条件下,我们推导了所提出GDRF估计器的统一Bahadur表示,并建立了相应统一置信带的有效性。包含了一个完全数据驱动的方法来选择下光滑调节参数和数据驱动的偏差控制置信带。模拟研究和应用展示了所提出方法的实用性。

英文摘要:

Ai et al. (2021) studied the estimation of a general dose-response function (GDRF) of a continuous treatment that includes the average dose-response function, the quantile dose-response function, and other expectiles of the dose-response distribution. They specified the GDRF as a parametric function of the treatment status only and proposed a weighted regression with the weighting function estimated using the maximum entropy approach. This paper specifies the GDRF as a nonparametric function of the treatment status, proposes a weighted local linear regression for estimating GDRF, and develops a bootstrap procedure for constructing the uniform confidence bands. We propose stable weights with minimum sample variance while eliminating the sample association between the treatment and the confounding variables. The proposed weights admit a closed-form expression, allowing them to be computed efficiently in the bootstrap sampling. Under certain conditions, we derive the uniform Bahadur representation for the proposed estimator of GDRF and establish the validity of the corresponding uniform confidence bands. A fully data-driven approach to choosing the undersmooth tuning parameters and a data-driven bias-control confidence band are included. A simulation study and an application demonstrate the usefulness of the proposed approach.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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