In isotonic regression discontinuity designs, the average outcome and the treatment assignment probability are monotone in the running variable. We introduce novel nonparametric estimators for sharp and fuzzy designs based on the isotonic regression which is robust to the inference after the model selection problem. The large sample distributions of introduced estimators are driven by scaled Brownian motions originating from zero and moving in opposite directions. Since these distributions are not pivotal, we also introduce a novel trimmed wild bootstrap procedure, which does not require additional nonparametric smoothing, typically needed in such settings, and show its consistency. We illustrate our approach on the well-known dataset of Lee (2008), estimating the incumbency effect in the U.S. House elections.
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