Jackknife variance estimation for multivariate statistics under hot-deck imputation from common donors

We consider a survey setting where missing values in a bivariate dataset are imputed by a hot-deck procedure which imputes all missing values for a given unit from a common donor with complete responses. It is shown that such an imputation procedure may lead to bias in standard estimators and a bias-adjusted estimator is derived. The variances of both the standard estimators and the bias-adjusted estimator are evaluated and jackknife variance estimators for each are constructed. We demonstrate the asymptotic unbiasedness of these variance estimators and illustrate their behaviour in a small simulation study.