Monotone functions arise naturally in scientific applications, including problems involving dose-response relationships, risk modeling, and survival analysis. Monotonicity constraints can enable valid inference on parameters for which fully nonparametric inference may otherwise be challenging. Generalized Grenander-type estimation provides a unifying framework for inference on monotone functions that naturally facilitates the integration of flexible machine learning tools while preserving valid large-sample inference. In this talk, we will review this framework, discuss ongoing extensions, and highlight how it can be used to develop inferential procedures for several problems arising in causal inference.
