With nonignorable nonresponse, an effective method to construct valid estimators of population parameters is to use a covariate vector called instrument that can be excluded from the nonresponse propensity, but are associated with the response even when other covariates are conditioned. The existing work in this approach assumes such an instrument is given, which is frequently not the case in applications. In this paper, we investigate how to search for an instrument from a given set of covariates, based on a pseudo likelihood approach assuming a parametric distribution of response conditioned on covariates and a totally unspecified nonresponse propensity. We propose a method and show that it produces a consistent instrument selection as the sample size tends to infinity, under some regularity conditions. The proposed method is examined in a simulation study and illustrated in a real data example.

中文翻译：

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不可忽略不响应的伪似然方法中的仪器搜索

对于不可忽略的不响应，构建总体参数的有效估计量的一种有效方法是使用称为工具的协变量向量，该向量可以从不响应倾向中排除，但即使在其他协变量受到限制时也与响应相关联。这种方法中的现有工作假设已经给出了这样的工具，但在应用中通常不是这种情况。在本文中，我们研究如何基于伪似然方法从一组给定的协变量中搜索工具，假设响应的参数分布以协变量和完全未指定的无响应倾向为条件。我们提出了一种方法，并表明它会产生一致的工具选择，因为样本量在某些规律性条件下趋于无穷大。