Unified framework for inference using confidence sets for the CDF

Oregon Convention Center 

Traditional statistical inference methods often face limitations due to their reliance on strict assumptions. Moreover, these methods are typically tailored to specific assumptions, restricting their adaptability to any alternative set of assumptions. In this work, we present a unified framework for deriving confidence intervals for various functionals (e.g., mean or median) under a broad class of user-specified assumptions (e.g., finite variance or tail behavior). Leveraging confidence sets for cumulative distribution functions (CDFs), this framework offers a principled and flexible inference strategy, reducing dependence on stringent assumptions and providing applicability in diverse contexts.

Confidence intervals

Assumption-lean inference

Confidence sets for CDF

Semi-infinite programming

Non-parametric methods 

IMS