Inference under imputation for missing survey data

尽管调查人员尽了最大努力使反应最大化，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，随着时间的推移，参与调查的人数正在下降，导致明显的无反应率。调查从业者区分单位和项目无反应。当在样品单元上没有获得测量值时，就会发生单元无响应。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回答时，就会发生调查中的项目不响应。它通常通过某种形式的输入来处理，其中包括“填充”缺失的值。如果对所有采样元素提供合适的辅助信息并适当地纳入到输入模型和/或非响应模型中，则输入可以有效地减少非响应偏差。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）将估算值当作真实值来处理可能会导致对估计器方差的严重低估，特别是在项目无反应率很明显的情况下；（iii）一些估算方法往往会扭曲所估算项目的分布。文献中已经考虑了解决(i)-(iii)的一些方面，并提出了一些解决方案。然而，有几个方面仍未解决。本研究的主要目标是追求迄今为止尚未考虑到的许多重要方向的技术发展。开发这些新技术应该能更好地理解作为一种处理项目无反应的方法的归算，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.