Isotonic subgroup selection

• 成果类型: Article
• 署名作者: Mueller, Manuel M.; Reeve, Henry W. J.; Cannings, Timothy, I; Samworth, Richard J.
• 署名单位: University of Cambridge; University of Bristol; University of Edinburgh; Heriot Watt University; University of Edinburgh
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkae083
• 发表日期: 2024
• 页码: 132-156
• 关键词: confidence-intervals; clinical-trials; least-squares; risk bounds; regression; CONVERGENCE; uniform

摘要

Given a sample of covariate-response pairs, we consider the subgroup selection problem of identifying a subset of the covariate domain where the regression function exceeds a predetermined threshold. We introduce a computationally feasible approach for subgroup selection in the context of multivariate isotonic regression based on martingale tests and multiple testing procedures for logically structured hypotheses. Our proposed procedure satisfies a non-asymptotic, uniform Type I error rate guarantee with power that attains the minimax optimal rate up to poly-logarithmic factors. Extensions cover classification, isotonic quantile regression, and heterogeneous treatment effect settings. Numerical studies on both simulated and real data confirm the practical effectiveness of our proposal, which is implemented in the R package ISS.