Isotonic subgroup selection
提出一种基于鞅检验和多重比较的等渗回归子组选择方法，能控制第一类错误且达到最优统计效率，适用于分类、分位数回归和异质性处理效应分析。
Abstract 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.