Inference under imputation for missing survey data

尽管调查人员尽了最大努力最大限度地做出反应，但几乎可以肯定的是，在大规模调查中会出现某种程度的无反应。最近的研究表明，参与调查的人数正在随着时间的推移而下降，导致明显的无回复率。调查从业者区分单位和项目无反应。当未在样本单元上获得测量结果时，单元无响应。在调查中，当抽样元素参与调查，但未能就一个或多个调查项目提供可接受的答复时，就会发生项目无响应。它通常是通过某种形式的归罪来处理的，这种归罪涉及“填充”缺失的值。如果对于所有采样的元素都有合适的辅助信息可用，并且适当地结合在估算模型和/或无响应模型中，则补偿可以实现无响应偏差的有效减少。然而，归因带来了一些重要的困难：(I)它扭曲了变量之间的关系；(Ii)将归因值视为真值可能导致对估计器的方差的严重低估，特别是在项目无响应率明显的情况下；以及(Iii)一些归因方法倾向于扭曲被归因项的分布。文献中已经考虑了涉及(I)-(Iii)的一些方面，并提出了一些解决方案。然而，有几个方面仍然没有得到解决。这项研究的主要目标是在许多到目前为止还没有考虑过的重要方向上追求技术的发展。开发这些新技术应该会更好地理解归因作为一种处理项目无反应的方法，并提供可能在调查过程中使用的新方法。

Despite the best efforts made by the survey staff to maximize response, it is almost certain that some degree of nonresponse will occur in large scale surveys. Recent studies suggest that participation in surveys is declining over time, resulting in appreciable nonresponse rates. Survey practitioners distinguish between unit and item nonresponse. Unit nonresponse occurs when no measurement was obtained on a sample unit. Item nonresponse occurs in a survey when a sampled element participates in the survey but fails to provide acceptable responses on one or more of the survey items. It is usually handled by some form of imputation which involves ''filling in'' missing values. Imputation may achieve an effective reduction of the nonresponse bias, provided suitable auxiliary information is available for all the sampled elements and appropriately incorporated in the imputation model and/or the nonresponse model. However, imputation presents some important difficulties: (i) it distorts the relationships between variables; (ii) treating the imputed values as if they were true values may lead to a substantial underestimation of the variance of the estimator, especially if the item nonresponse rate is appreciable and (iii) some imputation methods tend to distort the distribution of the items being imputed. Some aspects that address (i)-(iii) have been considered in the literature and some solutions have been proposed. However, several aspects remain unresolved.  The main goal of this research is to pursue the development of techniques in many important directions that have not been considered so far. Developing these new techniques should provide a better understanding of imputation as a method for treating item nonresponse and provide new methods that may be used in the course of a survey.