Confidence Intervals for Partially Identified Parameters
提出一种新型置信区间，以固定概率渐近覆盖参数真实值，而非覆盖整个识别区域，并修正了覆盖概率不统一收敛的问题。
Recently a growing body of research has studied inference in settings where parameters of interest are partially identified. In many cases the parameter is real-valued and the identification region is an interval whose lower and upper bounds may be estimated from sample data. For this case confidence intervals (CIs) have been proposed that cover the entire identification region with fixed probability. Here, we introduce a conceptually different type of confidence interval. Rather than cover the entire identification region with fixed probability, we propose CIs that asymptotically cover the true value of the parameter with this probability. However, the exact coverage probabilities of the simplest version of our new CIs do not converge to their nominal values uniformly across different values for the width of the identification region. To avoid the problems associated with this, we modify the proposed CI to ensure that its exact coverage probabilities do converge uniformly to their nominal values. We motivate this modified CI through exact results for the Gaussian case. Copyright The Econometric Society 2004.