Kernel-Based Density Estimates from Incomplete Data

SUMMARY The problem of using non-parametric methods to estimate multivariate density functions from incomplete continuous data does not appear to have been considered before. Methods of producing kernel functions on incomplete observations are suggested involving averaging over the missing variables or substitution of them by simulated values. Consistency of the procedures in terms of integrated mean squared error is investigated and optimal choice of smoothing parameter is discussed. Application in terms of imputation for missing values is discussed.