In a recent paper Speckman et al. (2002) introduced a technique for accounting co-variates when their effects are nonlinear. They proposed a test for a one-sided analysis of covariance which is based on a rank test for the residuals obtained by smoothing the dependent variable on the covariate....

A breakdown frontier is the boundary between the set of assumptions which lead to a specific conclusion and those which do not. In a potential outcomes model with a binary treatment, we consider two conclusions: First, that ATE is at least a specific value (e.g., nonnegative) and second that the...