Isotonic subgroup selection
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 multivari...
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Zusammenfassung: | 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
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DOI: | 10.48550/arxiv.2305.04852 |