On Kalman filtering and variances after single and multiple imputation
Using Kalman equations, we derive straightforward formulas for the total imputation variance for several imputation methods commonly used in regression analysis and (un)equal probability sampling without replacement in the case of nonresponse.
When observations in a survey are missing, one may use single imputation (SI) or multiple imputation (MI) for filling in the missing data. Using Kalman equations, we derive straightforward formulas for the total imputation variance for several imputation methods commonly used in regression analysis and (un)equal probability sampling without replacement. From these formulas it emerges that, in general, there is no necessity for taking parameter uncertainty into account. The paper proposes a new MI method which provides improved efficiency compared to the standard MI method for combining variances. Examples of the regression estimator for the unemployment rate and a simulation study are carried out to illustrate the theoretical results.
