Inference in a Class of Optimization Problems: Confidence Regions and Finite Sample Bounds on Errors in Coverage Probabilities
提出三种非渐近推断方法，用于解决部分识别参数的置信区间问题，适用于形状约束估计、离散博弈模型等场景，并给出有限样本下覆盖概率的下界。
This article describes three methods for carrying out nonasymptotic 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 structural parameters. Inference consists of finding confidence intervals for functions of 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.