Statistical Robustness of Stochastic Generalized Equations

H. Xu

Stochastic generalized equations (SGE) provide a unified framework for characterizing the first order optimality and equilibrium conditions of many decision making problems with random data.

The current research of SGE focuses on asymptotic convergence of the solutions obtained from solving the sample average approximated SGE (SAA solution in short) to the true solution of the SGE and uses the former to construct a confidence region of the latter.

A key assumption of the research is that sample data are generated by the true probability distribution which means that they do not contain noise.

In data-driven problems, data from real-world experiments are often corrupted with outliers and/or exhibiting heavy tails. In this project, we aim to address the issue by developing a new theory and method which builds upon robust statistics for analyzing SAA solutions in a data-driven environment where all data are potentially corrupted with applications in stochastic equilibrium problems and machine learning.