A penalized online sequential test of heterogeneous treatment effects for generalized linear models
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广义线性模型中异质性处理效应的惩罚在线序贯检验
- 研究问题
- 在线 A/B 测试逐批收集样本时，如何在高维协变量下识别异质性处理效应，并兼顾变量选择、检验功效与持续监测的错误率控制？
- 方法与思路
- 作者提出 POST 方法，将惩罚得分统计量与扩展的 p 值过程结合，用于广义线性模型中的在线序贯检验，并扩展至多重在线检验。
- 材料陈述的贡献
- 摘要称该方法具有选择一致性和较高检验功效，并控制第一类错误及多重检验的错误发现率；作者提供渐近分析、模拟和真实数据比较。
- 阅读关注点
- 应核对处理效应的参数化方式、惩罚与变量选择规则，以及持续监测和多重检验下错误率保证的具体条件与比较方法的设置。
- 阅读边界
- 这是 arXiv 预印本，不能据此确认同行评审或期刊接收；摘要未说明设计假设、维度增长条件或数值结果，功效优势仍需核对全文。
原文摘要
Identification of heterogeneous treatment effects (HTEs) has been increasingly popular and critical in various penalized strategy decisions using the A/B testing approach, especially in the scenario of a consecutive online collection of samples. However, in high-dimensional settings, such an identification remains challenging in the sense of lack of detection power of HTEs with insufficient sample instances for each batch sequentially collected online. In this article, a novel high-dimensional test is proposed, named as the penalized online sequential test (POST), to identify HTEs and select useful covariates simultaneously under continuous monitoring in generalized linear models (GLMs), which achieves high detection power and controls the Type I error. A penalized score test statistic is developed along with an extended p-value process for the online collection of samples, and the proposed POST method is further extended to multiple online testing scenarios, where both high true positive rates and under-controlled false discovery rates are achieved simultaneously. Asymptotic results are established and justified to guarantee properties of the POST, and its performance is evaluated through simulations and analysis of real data, compared with the state-of-the-art online test methods. Our findings indicate that the POST method exhibits selection consistency and superb detection power of HTEs as well as excellent control over the Type I error, which endows our method with the capability for timely and efficient inference for online A/B testing in high-dimensional GLMs framework.