Conventionally, regression discontinuity analysis contrasts a univariate regression's limits as its independent variable, "R," approaches a cut point, "c," from either side. Alternative methods target the average treatment effect in a small region around "c," at the cost of an assumption that treatment assignment, I[R<c], is ignorable vis-à-vis potential outcomes. Instead, the method presented in this article assumes "residual ignorability," ignorability of treatment assignment vis-à-vis detrended potential outcomes. Detrending is effected not with ordinary least squares but with MM estimation, following a distinct phase of sample decontamination. The method's inferences acknowledge uncertainty in both of these adjustments, despite its applicability whether "R" is discrete or continuous; it is uniquely robust to leading validity threats facing regression discontinuity designs.