Kernel imputation with multivariate auxiliaries

We consider a data set with missing observations but known auxiliaries for the sample and develop a real donor imputation. For each unit with missing observations we construct a distribution over a set of possible donors. We want the expectation (or distribution) to be chosen so that the expectation (or distribution) of the imputed values should equal the distribution of the units’ true values. This is obtained by letting the expected values of the auxiliaries equal the true value. Several kernel estimation features are introduced to reduce the bias associated with the unbalanced donor sets, due to sparse and bounded data sets. To get the good properties of kernel estimates to carry over, multiple imputation is used. Simulation studies indicate that our method has a good performance compared to competing methods. This is particularly noticable in notoriously difficult situations e.g. when the relationship between the study and auxiliary variables is nonlinear. The displayed simulations are based on two auxiliary variables, but the algorithm is generally formulated for any number of auxiliaries.