Inference with Survey Data Imputed by Hot Deck When Nonrespondents Are Nonidentifiable

Hot deck imputation for nonrespondents is often used in surveys. It is a common practice to treat the imputed values as if they are true values, and compute survey estimators and their variance estimators using standard formulas. The variance estimators, however, have seriously negative biases when the rate of nonresponse is appreciable. Methods such as the multiple imputation and the adjusted jackknife have been proposed to obtain improved variance estimators. However, multiple imputation requires that multiple data sets be generated and maintained and that the imputation procedure be proper; the adjusted jackknife requires \\ags" to identify nonrespondents. In many practical problems there is only a single imputed data set with unknown response status (no identiication ag). In this paper we derive some asymptotically design-consistent inference procedures in the situation where a stratiied multistage sampling design is used to collect survey data; hot deck imputation is applied to form a single imputed data set; the nonrespondents are nonidentiiable; and the survey estimators under consideration are functions of sample means, sample quantiles, and sample low income proportions.