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摘要翻译：
本文介绍了对一类最优化问题的解的部分辨识参数进行非渐近推理的三种方法。优化问题的应用包括形状限制下的估计、离散对策模型的估计和基于分组数据的估计。部分识别参数的特征是除了结构参数外，还包括观测随机变量的未知总体均值的限制。推理包括寻找结构参数的置信区间。我们的理论给出了在三组增加强度的假设下，置信区间的覆盖概率的有限样本下界。随着大多数经济学应用中的适度样本大小，随着假设的加强，界限变得更紧。我们讨论了种群参数的估计，并将我们的方法与获得部分辨识参数置信区间的其他方法进行了比较。蒙特卡罗实验和经验算例的结果说明了该方法的有效性。
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英文标题：
《Inference in a class of optimization problems: Confidence regions and
finite sample bounds on errors in coverage probabilities》
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作者：
Joel L. Horowitz, Sokbae Lee
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最新提交年份：
2021
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分类信息：
一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
This paper describes three methods for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation under shape restrictions, estimation of models of discrete games, and estimation based on grouped data. The partially identified parameters are characterized by restrictions that involve the unknown population means of observed random variables in addition to the structural parameters of interest. Inference consists of finding confidence intervals for the structural parameters. Our theory provides finite-sample lower bounds on the coverage probabilities of the confidence intervals under three sets of assumptions of increasing strength. With the moderate sample sizes found in most economics applications, the bounds become tighter as the assumptions strengthen. We discuss estimation of population parameters that the bounds depend on and contrast our methods with alternative methods for obtaining confidence intervals for partially identified parameters. The results of Monte Carlo experiments and empirical examples illustrate the usefulness of our method.
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PDF链接：
https://arxiv.org/pdf/1905.06491
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