Inference for Large‐Scale Linear Systems With Known Coefficients

This paper considers the problem of testing whether there exists a non‐negative solution to possibly under‐determined system linear equations with known coefficients. hypothesis arises naturally in number settings, including random coefficient, treatment effect, and discrete choice models, as well class programming problems. As first contribution, we obtain novel geometric characterization null terms identified parameters satisfying an infinite set inequality restrictions. Using this characterization, devise test that requires solving only programs for its implementation, thus remains computationally feasible high‐dimensional applications motivate our analysis. The asymptotic size proposed is shown equal at most nominal level uniformly over large distributions permits grow sample size.