Isotonic subgroup selection
Manuel M Müller, Henry W J Reeve, Timothy I Cannings, Richard J Samworth
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2025 · Volume 87 · Issue 1
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 .
Keywords
subgroup analysis, superlevel set estimation, isotonic regression, nonparametric inference, heterogeneous treatment effects
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