摘要翻译：
当条件变量为区间删失时，条件期望函数(CEF)最多只能被部分识别。当bins的数量很少时，现有的方法通常产生最少的信息边界。我们提出了三个创新点，使区间数据上下文中有意义的推理成为可能。首先，我们证明了删失变量分布已知的情形下的新的非参数界。其次，我们证明了在条件空间的一个固定区间上描述条件均值的一类测度通常可以紧有界，即使CEF本身不能紧有界。第三，我们证明了对CEF曲率的约束既可以收紧边界，也可以替代区间数据应用中经常提出的单调性假设。我们导出了使用前两个创新点的解析界，并发展了计算第三个创新点下界的数值方法。我们在仿真中展示了该方法的性能，然后给出了两个应用。首先，我们解决了死亡率作为教育函数的估计中的一个已知问题：因为高中或更低学历的人是一个较小的群体，因此随着时间的推移，他们的死亡率变化估计很可能有偏差。我们的方法使受教育程度保持不变成为可能，揭示了目前对受教育程度较低的妇女死亡率上升的估计在某些情况下有三倍的偏差。其次，我们将该方法应用于代际流动的估计，在许多没有匹配的亲子收入数据的情况下，研究人员经常使用粗略测量的教育数据。一旦考虑到间隔审查，像秩-秩相关这样的常规度量可能是不提供信息的；基于CEF区间的迁移率度量是有界的。
---
英文标题：
《Partial Identification of Expectations with Interval Data》
---
作者：
Sam Asher, Paul Novosad, Charlie Rafkin
---
最新提交年份：
2018
---
分类信息：

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。
--
一级分类：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
--
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
--

---
英文摘要：
  A conditional expectation function (CEF) can at best be partially identified when the conditioning variable is interval censored. When the number of bins is small, existing methods often yield minimally informative bounds. We propose three innovations that make meaningful inference possible in interval data contexts. First, we prove novel nonparametric bounds for contexts where the distribution of the censored variable is known. Second, we show that a class of measures that describe the conditional mean across a fixed interval of the conditioning space can often be bounded tightly even when the CEF itself cannot. Third, we show that a constraint on CEF curvature can either tighten bounds or can substitute for the monotonicity assumption often made in interval data applications. We derive analytical bounds that use the first two innovations, and develop a numerical method to calculate bounds under the third. We show the performance of the method in simulations and then present two applications. First, we resolve a known problem in the estimation of mortality as a function of education: because individuals with high school or less are a smaller and thus more negatively selected group over time, estimates of their mortality change are likely to be biased. Our method makes it possible to hold education rank bins constant over time, revealing that current estimates of rising mortality for less educated women are biased upward in some cases by a factor of three. Second, we apply the method to the estimation of intergenerational mobility, where researchers frequently use coarsely measured education data in the many contexts where matched parent-child income data are unavailable. Conventional measures like the rank-rank correlation may be uninformative once interval censoring is taken into account; CEF interval-based measures of mobility are bounded tightly.
---
PDF链接：
https://arxiv.org/pdf/1802.10490