Abstract Missing data is a commonly encountered problem in practice that can degrade the performance of predictive models and distort statistical inference. Many advanced imputation techniques suffer from a lack of interpretability, operating as “black boxes”. This paper introduces Parameter-based Imputation via Cycle-ensemble Averaging (PICA), a novel framework that first estimates distributional parameters directly from incomplete data and then performs imputation, offering a robust and transparent solution. PICA utilizes the direct parameter estimation method to compute the mean vector and covariance matrix. Subsequently, missing values are imputed using the conditional expectation within a cycle-ensemble strategy, which aggregates imputations from overlapping,...