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Multiple Imputation of Continuous Data via a Semiparametric Probability Integral Transformation

We propose a semiparametric approach incorporating principles of multiple imputation under the normality assumption, multivariate number generation, and computation of empirical cumulative distribution function (eCDF) values to impute continuous data with variables following any marginal distribution. This method involves mapping the data to normally distributed values, imputing these values, and back-transforming the data onto the scale of the original data. The transformations associated with eCDF computations constitute the nonparametric portion of our algorithm, while imputation under the normality assumption constitutes the parametric portion. Application of this method to simulated and real data leads to promising results.