论文标题
一个简单，简短但从未空的置信区间，用于部分识别的参数
A Simple, Short, but Never-Empty Confidence Interval for Partially Identified Parameters
论文作者
论文摘要
本文重新审视了对实价参数的简单但凭经验显着的问题，该问题通过渐近正常估计量通过上和下限部分识别。提出了一个简单的置信区间，并证明具有以下属性： - 它永远不会空或尴尬，包括当识别集的样本类似物为空时。 - 对于明确指定的伪特征参数是否有效，是否有效。 - 它不涉及调整参数和最小计算。 计算间隔需要集中一个标量滋扰参数。在大多数情况下，实际结果将很简单：要达到95％的覆盖范围，请向已确定的集合报告简单的90％（！）置信区间的结合，以及伪请参数的标准95％置信区间。 对于不相关的估计器 - 特别是如果从不同的子样本中估算界限以及常规的覆盖水平，则可以在分析中显示此简单过程的有效性。该案件在激励的经验应用中获得（De Quidt，Haushofer和Roth，2018年），其中证明了对现有推理方法的改进。更普遍地，模拟表明新型置信区间具有出色的长度和尺寸控制。这部分是因为，由于预计永远不会被空，因此可以将间隔比在样本空间的相关区域中的传统区间短。
This paper revisits the simple, but empirically salient, problem of inference on a real-valued parameter that is partially identified through upper and lower bounds with asymptotically normal estimators. A simple confidence interval is proposed and is shown to have the following properties: - It is never empty or awkwardly short, including when the sample analog of the identified set is empty. - It is valid for a well-defined pseudotrue parameter whether or not the model is well-specified. - It involves no tuning parameters and minimal computation. Computing the interval requires concentrating out one scalar nuisance parameter. In most cases, the practical result will be simple: To achieve 95% coverage, report the union of a simple 90% (!) confidence interval for the identified set and a standard 95% confidence interval for the pseudotrue parameter. For uncorrelated estimators -- notably if bounds are estimated from distinct subsamples -- and conventional coverage levels, validity of this simple procedure can be shown analytically. The case obtains in the motivating empirical application (de Quidt, Haushofer, and Roth, 2018), in which improvement over existing inference methods is demonstrated. More generally, simulations suggest that the novel confidence interval has excellent length and size control. This is partly because, in anticipation of never being empty, the interval can be made shorter than conventional ones in relevant regions of sample space.
