We introduce a test of the rank invariance or rank similarity assumption common in treatment effects and instrumental variables models. The test probes the implication that the conditional distribution of ranks should be identical across treatment states using a regression-based test statistic. When justified by the test, natural extensions of rank similarity partially identify the distribution...

This paper presents a new approach to the suucient conditions of nonlinear programming. Main result is a suucient condition for the global optimality of a Kuhn-Tucker point. This condition can be veriied constructively, using a novel convexity test based on interval analysis, and is guaranteed to prove global optimality of strong local minimizers for suuciently narrow bounds. Hence it is expect...

We describe an approach to statistically verifying complex controllers. This approach is based on deriving practical Vapnik-Chervonenkis-style (VC) generalization bounds for binary classifiers with weighted loss. An important case is deriving bounds on the probability of false positive. We show how existing methods to derive bounds on classification error can be extended to derive similar bound...