Inference for Large-Scale Linear Systems with Known Coefficients

Zheng Fang, Andres Santos, Azeem Shaikh and Alexander Torgovitsky

Papers from arXiv.org

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.

Date: 2020-09, Revised 2021-09
New Economics Papers: this item is included in nep-dcm and nep-ecm
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http://arxiv.org/pdf/2009.08568 Latest version (application/pdf)

Related works:
Journal Article: Inference for Large‐Scale Linear Systems With Known Coefficients (2023)
Working Paper: Inference for Large-Scale Linear Systems with Known Coefficients (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2009.08568

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