PDF(Pubmed)
Abstract：
Many partial identification problems can be characterized by the optimal value of a function over a set where both the function and set need to be estimated by empirical data. Despite some progress for convex problems, statistical inference in this general setting remains to be developed. To address this, we derive an asymptotically valid confidence interval for the optimal value through an appropriate relaxation of the estimated set. We then apply this general result to the problem of selection bias in population-based cohort studies. We show that existing sensitivity analyses, which are often conservative and difficult to implement, can be formulated in our framework and made significantly more informative via auxiliary information on the population. We conduct a simulation study to evaluate the finite sample performance of our inference procedure, and conclude with a substantive motivating example on the causal effect of education on income in the highly selected UK Biobank cohort. We demonstrate that our method can produce informative bounds using plausible population-level auxiliary constraints. We implement this method in the [Formula: see text] package [Formula: see text].
摘要：
许多部分识别问题可以通过集合上的函数的最佳值来表征，其中函数和集合都需要通过经验数据来估计。尽管凸性问题取得了一些进展，在这种一般情况下的统计推断仍有待发展。为了解决这个问题，通过对估计集的适当放松，我们得出了最优值的渐近有效置信区间。然后，我们将此一般结果应用于基于人群的队列研究中的选择偏差问题。我们证明了现有的敏感性分析，这些往往是保守的，很难实施，可以在我们的框架中制定，并通过有关人口的辅助信息提供更多的信息。我们进行了仿真研究，以评估我们的推理程序的有限样本性能，并在高度选择的英国生物银行队列中，以一个实质性的激励例子来总结教育对收入的因果影响。我们证明了我们的方法可以使用合理的总体级别辅助约束来产生信息边界。我们在[公式：seetext]包[公式：seetext]中实现此方法。
