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 pre-determined 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.

翻译：给定协变量-响应变量配对样本，我们考虑子群选择问题，即识别协变量域中回归函数超过预先设定阈值的子集。针对多元等渗回归背景下的子群选择，我们提出了一种基于鞅检验和逻辑结构假设多重检验过程的计算可行方法。所提程序满足非渐近的统一第一类错误率保证，其检验功效在仅相差多对数因子的情况下达到极小极大最优速率。该方法的扩展涵盖了分类、等渗分位数回归及异质性处理效应设定。基于模拟数据和真实数据的数值研究证实了我们方法的实际有效性，该方法已通过R包ISS实现。