Inference under imputation for missing survey data

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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.