Inference under imputation for missing survey data

尽管调查工作人员尽了最大的努力，以最大限度地提高答复率，但几乎可以肯定的是，在大规模调查中会出现一定程度的不答复现象。最近的研究表明，随着时间的推移，调查的参与率正在下降，导致明显的不答复率。调查从业者区分单位和项目无应答。当在样品单元上未获得测量值时，发生单元无响应。当抽样元素参与调查但未能对一个或多个调查项目提供可接受的响应时，调查中发生项目无响应。它通常通过某种形式的估算来处理，其中包括“填充”缺失值。插补可以有效降低无应答偏倚，前提是所有采样元素都有适当的辅助信息，并适当地纳入插补模型和/或无应答模型。然而，插补提出了一些重要的困难：（i）它扭曲了变量之间的关系;（ii）处理插补值，如果他们是真实的价值可能会导致大量低估的估计量的方差，特别是如果项目无应答率是可观的和（iii）一些插补方法往往会扭曲的项目被插补的分布。在文献中已经考虑了解决（i）-（iii）的一些方面，并且已经提出了一些解决方案。然而，有几个方面仍未解决。 这项研究的主要目标是在许多迄今尚未考虑的重要方向上寻求技术的发展。开发这些新技术应该提供一个更好的理解填补作为一种方法来治疗项目无应答，并提供新的方法，可用于调查过程中。

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.