Inference for Large-Scale Linear Systems With Known Coefficients

• 成果类型: Article
• 署名作者: Fang, Zheng; Santos, Andres; Shaikh, Azeem M.; Torgovitsky, Alexander
• 署名单位: Emory University; University of California System; University of California Los Angeles; University of Chicago
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA18979
• 发表日期: 2023
• 页码: 299-327
• 关键词: confidence-intervals; bounds; variables; identification; parameters; models

摘要

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.