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arXiv · 2009.08568

Inference for Large-Scale Linear Systems with Known Coefficients

Zheng Fang·Andres Santos·Azeem M. Shaikh·Alexander Torgovitsky
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Abstract

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

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Zheng Fang, Andres Santos, Azeem M. Shaikh, Alexander Torgovitsky. 2021-09-15. Inference for Large-Scale Linear Systems with Known Coefficients. https://arxiv.org/abs/2009.08568

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